Furniture, Wood and Cabinetry Finishing - Need help with chair repair

I have a dinner table chair with wooden arms. The arm was broken with the grain and made a pretty clean break. It is near the back rest but in a pretth thick part. I want to repair this but not really sure how. Any suggestions would be appreciated, Thanks

If you really want to try, you'd have to reinforce it with a dowel, inserted in each side, glue together using carpenter's glue (wood glue), then you'd have to refinish it by sanding and restaining. Maybe someone will step in and give you more detail on this as my knowledge is limited.
If it's a good chair, you might want to take it to a custom furniture guy or carpenter and he can make a new arm and re-attach to the chair.

Using wood glue, such as: titebond; and a method for clamping the piece in its original position should work.

The first thing to do is to determine how to clamp the piece. There are large clothes pin looking clamps at places such as Lowe's that will hold the pieces together. Strips of rubber under the clamps will keep them from slipping if this becomes a problem. Once you have this figured out, apply a coat of wood glue to the faces of the break and clamp the piece for at least an hour. Let the piece set for a day or so before putting it back into service.

There should be enough glue applied so that some squeezes out once the break is closed. The clamping force should be sufficient to close the break. Any glue that squeezes out can be wiped off with a damp cloth.

Hope this helps.