Public speaking is an important skill for career prospects and for leadership positions, but many people tend to avoid it because it generates anxiety. We run a field experiment to analyze whether in an incentivized setting men and women show differences in their willingness to speak in public. The experiment involved more than 500 undergraduate students who could gain two points to add to the final grade of their exam by orally presenting solutions to a problem set. Students were randomly assigned to present only to the instructor or in front of a large audience (a class of 100 or more). We find that while women are more willing to present face-to-face, they are considerably less likely to give a public presentation. Female aversion to public speaking does not depend on differences in ability, risk aversion, self-confidence and self-esteem. The aversion to public speaking greatly reduces for daughters of working women. From data obtained through an on-line Survey we also show that neither increasing the gains deriving from public speaking nor allowing participants more time to prepare enable to close the gender gap.