I know what you're thinking. "This should be in humorous guides."
No it shouldn't.
What you want anytime with Cho is CDR and AP. Noticing that attackspeed synergises really nice with Vorpal Spikes, Nashors Tooth is only an obvious choice. (Also note that Cho'Gath has the highest base AD on level 18.) And while you're at it, you might as well continue.

As a carry with Cho you have all you want: knockup+slow, silence, free life and damage. So go out there and kill stuff!

This build is not for high elo ranked play (at least i didn't test it there yet) but it's working fine in Summonerlevel 30 Normal games in both Summoners Rift and Twisted Treeline.

+ pushing/creeping is awesome
+ unexpected most of the time
+ really good melee carry

with good positioning: hitting one hits them all

- your skills don't nuke that much
- you survive a bit less

MPen, AP and dodge.
You can change dodge dunes to manareg but i wouldn't recommend it, especially since you have Nimbleness .

For Masteries i choose 9 21 0.
The defensive stats work fine with Cho'gath's Feast passive and Ardor increases the AS and AP gained. Also, if your team doesn't recognize you wanted to play AS, you can still tank that way.

Flash is pretty much staple and the debuffs on Exhaust help alot getting enemys down. I have no idea which other summoner spells could be a good choice.

Q, E, W then R > E > W > Q

You start out with Amplifying Tome, because on level 1 you don't use your Vorpal Spikes anyway.
Boots are important for chasing, positioning and in some minor cases getting away. Normally i don't need the Health Potion because of Cho'gaths passive, but in some cases it's pretty useful. If you feel safe, take a Mana Potion instead, early harassing with Rupture and a few attacks is powerful but expensive.

Malady is your first item. The early debuff helps a lot and also synergises fine with your skills and in best case also with those of your laning partner.

Berserker's Greaves. Yes, you can take Boots of Swiftness, but i personally like the attackspeed more. There's more movementspeed after you have your Phantom Dancer so you don't need Boots of Swiftness imo.

With Stinger, finally some CDR. Time to stack your Feast.

Vampiric Scepter for some lifesteal, you can skip this until after Nashors Tooth. I don't.

Nashor's Tooth. AS, AP, CDR. Any questions?

Phantom Dancer. AS and movementspeed.

Hextech Gunblade helps alot with survivability i guess. This is not confirmed though, because i always won before i could finish it.

Now you can start getting some defensive stats or build more AP. Rabadon's Deathcap will about double your AP and give loads to your damage output.

You are a carry. You are a pusher. You live because of your farm, so farm. Kill people with Feast. Use Feast as a free 1k Smite, if you want to. Remember, your team still needs your CC.