I love fighting GP because you can tell when they get pissed off that they just can't hit the barrel before you do. Then they start using multiple barrels, or just Q'ing you directly, which tickles unless they've a Sheen. Barrel chains can be played around by keeping an eye on where he puts the first (and second, if he's going for a 3-chain).
His Q has both a wind-up and a (very short) travel time, and his autoattack really doesn't have the best animation or attack point.
If you're melee, especially with an autoattack reset, 
etc.; the world's your oyster.
I complained to high hell and back about his barrels because they did so goddamned much but eventually I just got good at last-hitting the barrels. It becomes a mindgame after the first few.
You can:
- Time your autoattack to hit just as it ticks down.
- Start up your autoattack to hit it but stop it so he wastes his.
- Wait for it to tick down and auto + auto cancel.
- Wait for it to tick down and auto, auto cancel, but stop it so he wastes his.
- Walk away from where you think he's gonna place the next chain barrel, and fakeout a move to the wave so he wastes it.
Of course this just really applies to laning phase since later on when he has items, the barrels tick down too quickly (to make easy chains), and he's got so many of them ready, that it's really silly to try to break the barrels. He gets rewarded so much for popping one then compared to your payoff, for that risk.