Did the whole chuck (piece that holds the bits) break off or just the screw that holds the chuck?
Here is a Makita breakdown of your power tool so you can get an idea of what your Makita 6303 looks like and the part#'s you will need for replacement.
http://www.toolsandmachinery.com/index.php?cPath=2213_2262_2263_2265
Let me know if you have any other questions.
Don- www.toolsandmachinery.com, April 2009