There's certainly not going to be a compromise that gives Chabot more than a ~50% survival chance.
Even if you gerrymander the districts to try and get rid of Chabot, he’d still have a better than 50% chance of surviving unless you threw county and city lines out the window and drew him into Hamilton and Middleton. There are about 300,000 people who live in black, heavily Democratic areas and virtually everything else around is extremely Republican. To give him the boot without an equally hideous map, you would need a Democratic gerrymander and a 2008-style wave among black voters. The PVI in Hamilton County is incredibly misleading because it assumes a black turnout like 2008. If you drew a district entirely in Hamilton County including all the black areas and purposely cutting out the 80% Republican suburbs to keep the 65% Republican suburbs, you would still give Chabot about a 70% chance of getting re-elected just because the 2008 numbers are skewed in that area. And Steve Dreihaus isn’t exactly primed to make a comeback now that he’s suing the Susan B. Anthony List, so you would need to find a new candidate used to appealing to swing voters.
You don't need to gerrymander to get a district that would probably throw Chabot out. A district that excises the western suburbs in Hamilton County instead of the eastern ones (and is still entirely contained in Hamilton County and has very smooth edges following municipal boundaries) is just over 56% Obama and 53% generic Democrat. That's enough to make Chabot likely to lose (especially in a Presidential year), although certainly not guaranteed.
Not that there is any chance of the Republicans drawing such a district, of course.