1. Preheat oven to 350 degrees F; adjust oven racks to low and middle positions. Line baking sheets with parchment paper.
2. Whisk the flour, baking powder and salt in a small bowl; set aside.
3. Cream together the butter and both sugars on medium speed until light and fluffy, about 3 minutes. Beat in the eggs, one at a time, and then mix in the vanilla.
4. Stir in the flour mixture with a wooden spoon or a large rubber spatula, then stir in the oats and chocolate chips.
5. Using 2 heaping tablespoons per cookie, roll the dough into balls and place on the cookie sheets, spacing them at least 2 inches apart. Bake until the cookie edges are just turning golden brown, but the middles are still quite pale, about 12 to 14 minutes, rotating the sheets from front to back and top to bottom halfway through the baking time. Cool the cookies on the baking sheets for 2 minutes, then transfer to a cooling rack to cool for at least 30 minutes. Cookies can be stored in an airtight container at room temperature for up to 5 days.