Asking the search engine Google for "first Ph.D. in computer science Wexelblat" (without quotes) produces numerous sources saying the first Ph.D. in computer science was earned in December 1965 by Richard Wexelblat at the University of Pennsylvania. Changing the search from "Wexelblat" to "van Dam" says Andries (Andy) van Dam earned the second Ph.D. in computer science in May 1966, also at Penn. Their two degrees are from the Graduate Group in Computer and Information Sciences in the Electrical Engineering Department.
A similar search for "first Ph.D. in computer science woman" (without quotes) produces numerous sources saying the first Ph.D. in computer science to a woman was earned in 1968 by Barbara Liskov at Stanford. She was Barbara Huberman at the time and earned the degree from the Computer Science Department.
But at virtually the same time in June 1965, two other degrees were completed: Sister Mary Kenneth Keller, BVM, earned a Ph.D. from the Computer Sciences Department at the University of Wisconsin, and Irving C. Tang earned a D.Sc. from the Applied Mathematics and Computer Science Department at Washington University in St. Louis. [In an amazing coincidence, Keller and Tang received their doctoral degrees at commencements the same day, June 7, 1965. (Thanks to Vesna Kovach for this discovery.) -- RLL Sept 1, 2015] The purpose of this article is to show that in the United States, Keller and Tang were not just earlier but also first, thereby providing a more accurate historical record.
Although many believe it is of interest to know the first degree, a few say it does not matter. However, a first degree is sometimes noted in biographical information, either for oneself or for others. And judging from the interest and encouragement expressed when I sought people's help in determining the first degree, it apparently does matter to many, including buffs of computer science history.
Various definitions of a Ph.D. in computer science are possible. For this article, a computer science Ph.D. must be officially designated with "computer science" in the name of either its field or its awarding department (or program). First means the earliest officially designated computer science degree. Degrees not officially designated computer science are excluded, even with a thesis on a topic then or now considered to be computer science, because determining the first Ph.D. degree on a computer science topic would be difficult, if not impossible. It would be equally difficult to use the courses or examinations taken to determine the first. The definition of computer science Ph.D. is thus based on syntax, not semantics. Both Ph.D. and D.Sc. (Doctor of Science) degrees are included; Ph.D. is used for both. Honorary degrees are excluded.
Using this definition, Keller and Tang earned computer science Ph.D. degrees, as did Wexelblat, van Dam, and Liskov. For these five degrees, the field is the same as the department. Wexelblat, van Dam, and Liskov each relied on statements made by others and never saw the need to research the issue. Additional information about the first degree is available. 
Others have discussed the question of who was first. Amber Bouman  recognizes Keller as the first woman while noting that Barbara Liskov is often cited as the first woman. For her guest lecture in computing history, Katherine Deibel  includes on two slides,
Sister Mary Kenneth Keller: First woman to earn a Ph.D. in Computer Science (University of Wisconsin-Madison). . .
The First Ph.D.s in Computer Science? The first Ph.D.s designated as "Computer Science" were awarded by the University of Pennsylvania: Richard Wexelblat (December, 1965), Andries van Dam (May, 1966). Keller earned her Ph.D. in May [sic], 1965 from the University of Wisconsin-Madison.
Twelve schools, listed below with first graduates, had established computer science departments or programs by the end of 1965. Given Keller's and Tang’s degree dates of June 1965 (and assuming no other school had a pre-1966 department), these are the only possibilities that could have awarded the first computer science Ph.D.
The data on early departments and first graduates are the result of extensive searches through many sources. Possible schools came mainly from works by Aaron Finerman  and Robert Gensler . Finerman included a chapter on "Organization" by Frank Beckman (pages 48-58) and a table of "U.S. Institutions Offering Degree Programs in Computer Science" (pages 217-220). Gensler listed "Miami University founded 1963," but I found no pre-1966 Ph.D. department at either Miami University (Ohio) or at University of Miami-Coral Gables.
To help find data and determine pre-1966 departments, I contacted early computer science Ph.D.s for their recollections and suggestions. Web search was crucial, as expected. Several Ph.D. graduates searched Web sites of their degree-granting departments or used other knowledge to provide full or partial information. Other department Web sites provided information, sometimes even a history. So did department anniversary celebrations, whether recorded electronically or on paper. Searching university libraries online gave dates for some degrees, suggested whether degrees were computer science, supplied names of relevant graduates and sometimes indicated the absence of degrees before the end of 1965. The Mathematics Genealogy Project  with its varied searches proved very useful. Emails sent to people who might have knowledge yielded results, as did emails to possible departments. As with any historical study, it was necessary to interpret and resolve conflicting information.
Here, then, are the twelve computer science departments or programs (plus entries for Princeton and North Carolina) founded pre-1966 with their first degrees (preserving whether "Science" in a name is singular or plural). The order is generally by date founded. The degree date could be date of graduation, defense, or when all requirements were met, including library filing. Some dates do not include a month, another reason the dates are not strictly comparable.
Stanford had a Computer Science Division in the Mathematics Department starting in 1961. The division awarded masters degrees, but I found no Ph.D.s from the division. Ph.D.s apparently continued as standard mathematics degrees until the Computer Science Department started in January 1965.
Information is included for Princeton, North Carolina, Michigan's Communication Sciences (program and department), and Carnegie Mellon's Systems and Communications Sciences, even though "computer science" is not part of the names of fields or departments; these degrees are excluded in determining the first. Michigan and Carnegie Mellon are listed by the department dates rather than program dates. From the start, I intended to exclude the Systems and Communications Sciences program. But including the others led me to add Carnegie Mellon's Systems and Communications Sciences.
Thus Sister Mary Kenneth Keller and Irving C. Tang are the first to earn computer science Ph.D.s in the United States. Even though my search for data was thorough, I welcome improvements to the historical record that refute the conclusion or add data. Note that although I found no woman after Keller and before Liskov, there may be one or more because I searched only for the first degrees and thus stopped short of determining the second woman.
For their significant help in various ways in uncovering material, understanding it, and then presenting it, I am grateful to Ed Lazowska, Barbara Liskov, Bobbi London, Jude Shavlik, Larry Travis, Andy van Dam, Dick Wexelblat, Bill Wulf, and Bryant York.
All Web pages were accessed November 21, 2012.
[1.] Amber Bouman, "The 15 Most Important Women in Tech History," March 2011, http://www.maximumpc.com/article/features/15_most_important_women_tech_history
[2.] Katherine Deibel, "Women in Computing," Guest lecture in CSEP 590, A History of
Computing, University of Washington, November 2006, Slides 25 and 26.
[3.] Aaron Finerman (ed.), University Education in Computer Science, Proceedings of Graduate Academic Conference in Computing Science, Stony Brook, New York, June 5-8, 1967, ACM Monograph, Academic Press, N.Y., 1968.
[4.] Robert Gensler, "The IBM 650: Little Computer, Big Impact," Paper for CS 630, The
"Science" of Computer Science, University of Arizona, Fall 2007. http://www.cs.arizona.edu/classes/cs630/spring07/ (Select Final Papers and then Robert Gensler.)
[5.] Ralph L. London, "Additional Information for 'Who Earned First Computer Science
Ph.D.?,'" December 2012, http://www.clarke.edu/media/files/Academics/Departments/Computer_Science/First%20PhD%20Additional%20Info.pdf
[6.] "Mathematics Genealogy Project," www.genealogy.math.ndsu.nodak.edu
Ralph L. London is an adjunct faculty member with the Computer Science Department at Portland State University, Portland, Ore. Portions of this post previously appeared at http://firstcomputersciencephd.blogspot.com/.