[Since I couldn't find much about this particular HP/X combo, I thought I'd try writing a strategy article...]
This HP/CH combo is simple: with 8 Coppers, a CH, and ~5 HPs in your deck, you are basically buying a Province every turn. The question is, how do you (quickly) get to that point?
A Silver/trasher or Silver/Silver opening should give you enough econ to continually buy HPs after Turn 5. If you open 5/2, you might as well take HP/Copper, especially if there is no trashing and you're each playing a solitaire game. You can also be ballsy and try opening Copper/trasher as well, but Silver/trasher is usually the better choice since you can just trash your Silver once you have a few HPs. After you have about 5 HPs, if you haven't yet, buy a single CH and your 8th Copper. Your HPs will send everything to the discard so your CH lets you buy a Province each turn. Assuming little to no interruption and average luck, this combo can easily snag 4 or more Provinces by Turn 15 and isn't slowed down as much as other engines are during the greening phase as long as you don't panic and buy Duchies too early.
Trashing all of your early Estates goes a long way to boosting this strategy as they won't factor into your HP search. Salvager does this best, as it can often boost you to $5 on Turn 3 or 4 while getting rid of your unwanted cards. Forager is also a noteworthy mention as it is a non-terminal trasher that will usually net you $1 and could be useful in games with light junking. Both Salvager and Forager also give you a +Buy when you're ready to buy CH and your 8th copper. Bishop can work decently as well and basically does everything Salvager does in Shelter games and your opponent might even help you trash your Bishop when you're done with it.
What if you don't end up with $5 on Turns 3 and 4? You're a little bit behind where you'd like to be, but this is usually not an issue as long as you keep trashing your Estates/Shelters. You can also consider picking up sifters such as Warehouse if they're available, since getting $5 is much easier if you can choose 4 cards out of 7, particularly in games without trashing. Sifters can also trade Coppers in your hand that you don't need for HPs when you're greening. Sages can be useful if there are no other cyclers on the board, as they can get to your Silvers and HPs early and you'd rather have Sage pick up a Province (as opposed to HP doing so) after you've built up your combo anyway. Schemes can ensure that, once you start buying Provinces, you start with more HPs in your hand since you reshuffle every time you buy a Province. 3 Schemes and 6 HPs basically guarantees you a Province every turn. However, be careful how many unique cards you pick up, since they could clog your HP chain.
What this combo despises (like most HP/X combos) is junking attacks. Don't even try it if there are cards such as Marauder, Ambassador, or Swindler on the board. Cursers such as Torturer are slightly less problematic, since as long as you have a Curse in your hand, you will bypass most of your remaining Curses, but powerful early game Cursers such as Sea Hag will cripple your chances of consistently getting $5 with your 7 Copper/1-2 Silver econ. Unreliable Cursers such as Jester are not a huge deal since you're trashing your Estates early and you were going to buy that 8th copper anyway.
Works well with:
* Cheap trashers that can be bought on Turn 1-2, particularly Salvager.
* Cyclers such as Warehouse and Cellar (and Storeroom if you have the spare Action)
Decent with:
* Sage
* Scheme
Does well against:
* BM strategies
* Most engines that rely on Provinces as their source of VP
* Most strategies that require a buildup of many cards, such as Silk Road- and Philo Stone-centered strategies.
Not really affected by:
* Top deck attacks and discards such as Rabble, Tribute, Scrying Pool, and Noble Brigand
* Discard attacks (2-3 HPs can all but guarantee a Province; Margrave could even be helpful)
* Cutpurse
Soft-Countered by:
* Targeted trashers, such as Saboteur and Knights
* Slow or Unreliable Cursers such as Torturer and Jester
* Governor, Embassy
* Alt-VP strategies that can sit back and force you to buy all of the Provinces, such as mass Goons
* Alt-VP strategies that require cheap cards to quickly gain loads of VP, such as NV/Bridge and HT/Duke/Duchy
Hard-Countered by:
* Junking attacks with variety such as Marauder, Swindler, and Ambassador
* Early and strong Cursers such as Sea Hag and IGG/Duchy
* Fast rushes such as IW/Gardens
Remember that HP/CH works best when there are as few unique cards (indeed, as few cards) in your deck as possible. The more non-HP cards in your deck, the greater chance that you get a hand of 0 or 1 Hunting Party after your reshuffle. If you think you're sufficiently ahead of your opponent, consider trashing your first Province or two if it means that you won't have Provinces clogging up your HP chain. You don't need 4+ Provinces to win; you just need more VP than your opponent. Salvaging Province #1 to buy Province #2 might be better than keeping Province #1 and using CH to buy Province #2 if you need to close out the game before his lategame megaturn(s). If you have the Actions to spare, using TFBs such as Bishop or even Forager on your first Province might be a smart idea.
