While education levels of women have increased dramatically relative to men, women are still greatly underrepresented in Science, Technology, Engineering, and Mathematics (STEM) college programmes. We use unique data on preference rankings for all secondary school students who apply for college in Ireland and detailed information on school subjects and grades to decompose the sources of the gender gap in STEM. We find that, of the 22 percentage points raw gap, about 13 percentage points is explained by differential subject choices and grades in secondary school. Subject choices are more important than grades -- we estimate male comparative advantage in STEM (as measured by subject grades) explains about 3 percentage points of the gender gap. Additionally, differences in overall achievement between girls and boys have a negligible effect. Strikingly, there remains a gender gap of 9 percentage points even for persons who have identical preparation at the end of secondary schooling (in terms of both subjects studied and grades achieved); however, this gap is only 4 percentage points for STEM-ready students. We find that gender gaps are smaller among high-achieving students and for students who go to school in more affluent areas. There is no gender gap in science (the large gaps are in engineering and technology), and we also find a smaller gender gap when we include nursing degrees in STEM, showing that the definition of STEM used is an important determinant of the conclusions reached.