In a medium bowl, cream together butter, brown sugar and white sugar. Mix in the egg and vanilla. Combine flour and bicarb soda; blend into creamed mixture. Stir in the rolled oats, coconut and white chocolate chips. Drop dough by rounded tablespoonsful onto ungreased baking trays.
Bake for 10 to 12 minutes in preheated oven, or until lightly browned. Cool on wire racks.