You want to have a certified arborist look at your tree. Be careful, a lot of the certified arborists here work for 'tree service' companies that are in business to remove trees. So if there's any doubt, get a second opinion, too. It's really important to ask to see the person's current certification, needless to say.
From the picture of the healthy leaves you showed, it looks like the tree is still growing. There may be a good chance it will survive, but as porkpal said, the branches on the wounded side might die off and it could develop somewhat lopsided, so look at it from the standpoint of being off balance, as well. If there's any chance it would fall on something or injure anyone, you should then take that into account when you are deciding what to do about it.
