This is repair we did 4 years ago.
We didn’t rebuild the chimney, but patched it. If you look closely, we colored the patch in bricks to make repair nearly unnoticeable. This is a relatively inexpensive repair, much less than rebuild. With regular maintenance this chimney could last quite a while, but without maintenance, water could continue to get in, moisten the rebar which rusts, expands and breaks bricks and mortar joints.