Preheat oven to 350°F. Grease an 8-inch square pan.
Melt chocolate chips and butter over low heat in a double boiler or small metal bowl over simmering water.
In a large bowl, using an electric mixer on medium speed, beat eggs with sugar until thick. Stir in flour, baking powder and salt. Add chocolate mixture and vanilla; stir well. Stir in walnuts. Pour batter into pan and bake until toothpick inserted in center comes out clean, 20 to 25 minutes.