Shin splints is caused by stress damaging the delicate tendons that bind the muscle tissue to the shin bone. This is typically caused by high impact forces from running.
Have you followed the golden rule and not increased your mileage (or time on your feet) by more than 10% per week ?
The other thing to look at is your technique and running shoes. Conventional wisdom (sponsored by Nike) is that you need thick soled 'cushioned' soles for stress injuries like shinsplints. More recent research, however, suggests that this is counter productive since fat soles and a high heel lift in particular impede the foots natural shock absorption mechanism which is to use the calf muscles as shock absorbers.
Try this free ebook for more information on correct technique and footwear.