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