Unless you're eating gallons of it a day, no: peanut butter is not fattening on its own. On 2 tablespoon serving only has 3.3 grams of saturated fat and 12.3 grams of unsaturated fat, about the same as olive oil.
Too much of anything can be fattening. Peanut butter is no exception. While peanut butter does have a lot of good things going for your body, eating too much of it without getting exercise can be fattening.