Mix yeast, sugar, and water in a large bowl. Let sit for five minutes. Add milk, eggs, sugar, oil, salt, and vanilla. Stir in flour a cup at a time. Add enough to get a soft dough. Knead till smooth. Place dough in a greased bowl and let rest for about 20 minutes.
Roll dough out on an oiled counter to a rectangle about 13×28″. Spread melted butter evenly over the top of the dough. Sprinkle sugar, coconut, and chocolate chips evenly over dough. Roll dough up and seal the edge by pinching. Cut into slices 1″ to 1 1/2″ thick.
Place on a greased cookie sheet with sides. Cover with waxed paper and let rise till doubled, about 45-60 minutes. Bake at 350° for about 30 minutes or till lightly browned.
Melt chocolate chips in a ziplock bag in the microwave at 50% power, squishing every 30 seconds till smooth. Cut a small hole in the corner of the bag. Drizzle melted chocolate over the warm rolls.