No doubt endgame Chogath is a beast; I've been in several games where he's at 5000+ life, and I've seen a lot of builds with him having at least 1-2 beefy armor items too. I've had him tank towers while our entire team hurls themselves against him to no avail. This is a problem with a few other heroes, but I haven't seen it so prevalently as it is with him. Does anyone have an effective way to counter him endgame or do you just have to shut him down as fast and hard as you can the whole match?

Don't ignore him. Since each team should have at least 2 clairs, try and catch him while he's trying to fill up his warmogs (assuming you couldn't shut him down early). In a team battle, burn down the softies and retreat if you get close to the feast hp mark. Chogath is worth focusing before some other targets since if you kill him you reduce his effectiveness for the next 5 minutes or so.

The reason not to ignore him in large team battles is that when a good Chogath finishes his warmogs and sunfire, his next item happens to be an atmas, which doubles his damage output to around 220. Not a joke, and if you get low he will flash/walk up to you and eat you.

I play Cho'Gath and got wrecked by an evasion Jax yesterday. The guy said he had 42% dodge by the end of the game. We had three heroes on him and he killed us all. It was just sad, really.