Place butter and chocolate chip in a medium size, microwaveable mixing bowl. Microwave on high for 30 seconds. Stir, and continue microwaving and stirring in 30 second intervals until chocolate is melted.
Beat in sugar, then vanilla and eggs, until well combined.
Stir in flour until just combined.
Pour into a well greased 8"x8" pan. Bake in the preheated oven for about 35 minutes or until a toothpick inserted into the center comes out clean.
Cool completely before cutting.
Notes
I like to line my pan with enough overhang to remove the entire baked and cooled pan of brownies. This makes it much easier to slice.