Preheat the oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a medium bowl, mix together the coconut, sweetened condensed milk, and vanilla until well blended. Drop by teaspoonfuls, one inch apart, onto the prepared cookie sheets.
Bake for 10 to 12 minutes in the preheated oven, or until edges are slightly browned. Using a moistened spatula, remove at once from baking sheets. Cool on cooling racks until firm. Store in a covered container at room temperature.