Beat peanut butter, butter, and sugars at medium speed with an electric mixer until creamy. Add eggs and vanilla, beating until blended.
Combine flour, soda, and salt in a small bowl; gradually add to butter mixture, beating well. (Dough will look a little moist.) Stir in morsels. Drop by tablespoonfuls onto lightly greased baking sheets.
Bake at 350° for 8 to 14 minutes or until desired degree of doneness. Remove to wire racks to cool completely.