Couple of notes.
Keep-away is the main goal, but you don’t want to turtle up. Sometimes the Gief player might feel he can comfortably stay 3/4th-full screen and build meter with KKK lariat. Use Chun’s fast walking speed to punish or force a block if he starts doing this. EX Hand is the best weapon the Gief player has for breaking through Chun’s wall of pokes. You need to stay off your back as much as possible and EX hand is going to put you there in a hurry.
Mixing up pokes is important, it prevents them from properly timing st. MK or cr. RH from stuffing you. Throwing in fireballs is fine, but be careful at what ranges you use them. Out of position fireball and sweeps are probably the top 2 ways Chun gives up all the advantages she has over Gief in a poke battle.
If they just decide to tank it through, and a lot of Gief players will do this, using normal green hands and RH then you can take advantage of this behavior without too many issues. Properly timed sweeps are hard to punish and throws are great on blocked green hands. You can also sometimes do a walk-up throw without repercussion, due to the speed which you can get point blank and Gief’s are unlikely to standing SPD on reaction due to the possibility of a whiff.
Neutral jump RH is also a big deal, because it provides a safe-zone. Gief only has 3 real options that work against it. They can try a max range St. RH which will usually get stuffed. They can walk right next to Chun’s foot and cr. mk and that will usually beat it, but doesn’t do a lot of damage and doesn’t get them point blank without a green hand follow-up, which is unsafe. Finally if they time EX hand right, they can either beat it or space it in such a way that the RH whiffs and they can SPD when you land. Naturally the latter is the scary part, since it basically mocks you for trying the jumping RH. However Gief can only try it once or twice and if they get the timing wrong they eat a full jump-in combo and have to try and get in from max range again. Since it requires meter for them to try this approach, you can sometimes spam neutral RH without a ton of ramifications. Add in an empty jump or two and on occasion you can even catch Gief open if they try a late poke and whiff.
EX SBK is obviously your best move if you get knocked down, but you can’t afford to abuse it. At some point Gief is going to get smart and jump-in with a back-MK and stuff EX SBK clean, leaving you out a bar, a little lower in life and Gief point blank in your face. Sometimes the best move is just to block the cross-up and go for a jump back RH, sometimes it’ll get stuffed and sometimes you escape. One move which I’m unsure is an option is I accidentally threw out normal SBK and obviously got hit by body splash. However since I got air recovery the typical follow-up from gief was mistimed and allowed me to punish him severely. If normally SBK consistently gets you an air recovery that might be good enough as it provides a slight space buffer and forces the gief to be on his toes.
I don’t see many Chun save up for super in this match and although I can sort of understand why (ex SBK) it really is one of the best punishes she has. It’s not very hard to hit, punishes like 2/3’rds of Gief’s moves if they whiff and basically shuts down the tank approach, forcing him to be patient and poke back until he can get very close.
tl;dr version.
Tank Gief is a lot easier to beat because he runs into pokes all day. Mix them up so the green hand timing is off and don’t let him build free meter so he only has like 3 chances to EX GH. Neutral Jumping RH can be a huge annoyance, especially if you’ve forced Gief near a corner. because he takes a lot of free damage, a knockdown into a jump-in combo can basically KO him since he then has to chase you all across the screen again to do anything.
Pokey Gief is harder to stop, but again is relying on timing his attacks better than you or making a correct guess. This approach is also more likely to eat silly things like walk-up throws, EX Ball or back jump RH. Key is to keep working with it and changing it up. The worst thing you can do is whiff a bunch of short quick recovery moves because you aren’t going to bait an EX Hand, instead he’ll walk up slightly and most likely max range SPD you. Even if he screws up, you aren’t at a great punish range so what does he care?
EX SBK is the nuts on wake-up, but be wary of a late jump-in. If you can see the MK coming, you can take advantage of it and get away clean.
Super is v.v. good.
Sweep is probably the most overrated poke in the match, same with cr. mp which some people use for w/e reason.
quick edit; Chun’s FA is pretty good against Gief. It can force players not to spam quick standing pokes and even a lvl1 FA on block is completely safe for Chun. Just be very ready to backdash if he just keeps walking forward or he gets a free throw or SPD.