The term "gender gap" refers to the significant underrepresentation of females in many subjects. In Computer Science, the gender gap exists at all career levels. In this article, we study whether there is a performance gap in addition to the gender gap. To answer this question, we analyzed statistical data on student performance in Computer Science from 129 universities in the United Kingdom covering the years 2002 to 2013. We find that male students were awarded significantly more first-class degrees than female students. We evaluate four other subjects--Subjects Allied to Medicine, Business & Administrative Studies, Mathematical Sciences, and Engineering & Technology--and find that they do not exhibit this performance gap. From this finding, we review explanations for the gender and performance gaps, as well as potential solutions to eliminate the gaps. Most solutions do not require major institutional change and could thus be implemented easily.