The risk of a young woman having a stroke is very small if she is not a smoker. Smoking increases this risk and women who smoke should not take the Pill because it increases the risk of both heart attacks and strokes. Even the low dose oral contraceptive is not completely safe in smokers.
A woman under age 35, who does not smoke and has longstanding migraine headaches without "aura" may be prescribed OCPs because the risk of stroke is small in this group. New migraine, however, is an indication to stop the pill and use another form of birth control.