Yeah, these Chuns are tricky and you need a lot of patience. It’s a battle of life lead and who needs to get in… In general, try to squeeze out some dmg early on, but do not take much risks, as the life lead will win in that match up.
I try to stay out of poke range, as Chun wins the poke game in general. Fireball zoning and Anti Air until you can score a hard knockdown. Then hit and run tactic as Chun’s EX SBK can be easily safe jumped (punish with cr.hk or ex tatsu), but beware of DWU and her backdash in cr.hk or Hazan. Not sure if her b.dash can be properly OSed. But in general you do not want to be close to her outside of knockdown mix ups or then you lost the life lead.
Close range Hados can be risky due to her fast (focus) dash in. More so cr.mp x Hado strings as the Hado then also gets telegraphed. Try to poke her at absolut max range of far.mk as sort of a walk in stopper, but she can duck it and it is vulnerable against her sweep or cr.mp and whiff punishable of course. You can also poke check her with max range far.lk chained in cr.lk, good range, fairly quick, pretty safe and beats focus. If she mashes sweep after that you should be able to whiff punish it. Smart, sparingly used focus fishing can also help, as Chuns relys on one hit pokes at certain ranges and particularly if she likes to always press buttons after she blocked one of your pokes.
During ground game Chun can not jump at Gouken at all, on reaction you can always jump MP 2hit in juggles, amongst other U2 and Super. After you gained U2 or Super, she must fear that and stay on the ground. AA Ex Tatsu also works of course, but I would try to safe meter for ex tatsu fadc or super. But Ex Tatsu her neutral jumps when up close. But do not jump in on her either (outside of kd), as her jump double HP in juggle really hurts.
Try to bait an anti fireaball Hazan Shu here and there, it’s mildly punishable with FA1 backdash. A whiffed Far.MP looks similar like the Hado start up. Also jump ins into AA can be baited that way if your opp relies a lot on twitch reactions.
Chuns like her cr.lk and cr.lp, if you have a good read LP Kongo it, but comes with a lot of risks of course. But particularly rewarding close to corner when FADCed. If Chun uses her slow fireball as shield during groundgame, MP Kongo the fireball. Only hits once though, if she does not know already anyway…
I recommend OS trowh tech cr.mk, as it has 4fr start up and can be OSed in HADO which combos on counter hit. but limited horizontal range and on whiff easily punishable. If you sure about an incoming tick throw attempt you can try to instant air backjump HK which can hit the whiff throw animation then. But comes with risks obviously. Neutral jump HP will not hit Chun in time, she can block until then and maybe even punish with EX SBK. If your meter management was right (you should not have much possibilities to meaningful spend meter in that match up anway) you can try to ex tatsu fadc her throw attempt at least once in a round. Save for it, she must fear it, so that she thinks twice about going for tick throws.
I am surprised she does not use U1 in that match up, but this helps you in your zoning attempt. So do not jump in her double HP in U2 and try to to keep her out so she has no possibilty to cr.lk - ex legs - U2. LP Kongo can help with this too, even though risky.
Just my 2cents, I hope this helps a bit…
EDIT
If she jumps over your fireball, you should almost always still have the time to ex tatsu or kongo her jump in.