We investigate whether having an advisor of the same gender is correlated with the productivity of PhD science students and their propensity to stay in academic science. Our analysis is based on an original dataset covering nearly 20,000 PhD graduates and their advisors from U.S. chemistry departments. We find that students with an advisor of the same gender tend to be more productive during the PhD and more likely to become professors themselves. We suggest that the under-representation of women in science and engineering faculty positions may perpetuate itself through the lower availability of same-gender advisors for female students.