Preheat oven to 375 degrees F (190 degrees C). In the microwave or over a double boiler, melt unsweetened chocolate and butter together, stirring occasionally until smooth. Sift together flour, baking soda, baking powder, and salt; set aside.
In a medium bowl, beat sugar, eggs, and vanilla until light. Mix in the chocolate mixture until well blended. Stir in the sifted ingredients alternately with sour cream, then mix in chocolate chips. Drop by rounded tablespoonfuls onto ungreased cookie sheets.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely. Store in an airtight container.