Is there a ',' needed in this sentence?
My chair which is broken is make of wood.
You must have either two commas or none.
If you mean that it is specifically your broken chair which is made of wood, and you are not talking about any of your other chairs, then which is broken is not set off with commas: it is a restrictive clause, which tells the reader that you are only talking about that particular chair.
If you mean merely that the chair which is made of wood happens to be broken, then which is broken is a non-restrictive clause and it is set off with commas, like this:
My chair, which is broken, is made of wood.