I'm not seen Chansey as something that can "struggle" your teambuilding, actually, almost any balanced and offensive team should have wallbreakers for it's partners, because and otherwise, a sweep or just a general efficience is impossible, what is the difference with Chansey? It "usually" check a lot of things, the key word should be "usually", because you can beat the blob with a good number of ways:
1. Trick, Thief, Knock Off just cripple her for all the match, seeing the fantastic distribution of those move, you can perfectly use them on 1-2 of your Pokémon, or on your Special Sweeper, and make with a simple move the game an almost 6vs5, easy, doesn't it? Even if Chansey switch-outs predicting it, it's partner will be on the danger of lose it's item, a bad thing for sure. Of course, you can overpredict Chansey, too, just using the move when you think she will switch-in (after all, people switch-in her with all careless).
2. Generally, any user of Taunt can beat her, physical or special one, and more if you're using a trapping move like Mean Look, of course, it's not a so common option, but it works not only with Chansey, but with almost any wall, so, it's a good option to have on almost any team.
3. Chansey is not the unique special wall of the game, we have some premiers over there like Slowking (who had also Regenerator), and usually, your special sweeper will be unnable to sweep until you beat it's check, that's something normal, sweepers have checks, otherwise we could just spam powerful moves and win the game without any need to think. Chansey checks more threats, but almost all she does is to check them and use paralize support, because she can't do anything else at all, at the difference of other special walls.
4. Usually, when Chansey is alone, she will lose the game, because she can't beat anything on 1vs1 at all. And if she doesn't end alone at the end of the game, then it means you beated her before, and thus, making your path to just special sweep to the oblivion the opposition, because teams with Chansey doesn't tend to have more checks to special attackers, and thus, you have almost the victory winned.
5. Ground Type Pokémon leave Chansey without any chance to do nothing, so, any Ground Type Pokémon will check her to the end of times, same goes for Limber users, not the best thing, but it seriously comes handy.
6. On general, a balanced team should have clerics, because Chansey is not the unique thing that can spread burn/paralize to the team, and balanced teams doesn't tend to have too many raw power to just destroy everything before it happens, and clerics are the Chansey's number one issues to make a help to it's team.
7. If she wish pass, you can easily predict it and destroy the switch-in or switch to it's counter, like the move Protect, it can comes like a double-edge sword.
8. Toxic Spikes make her almost a dead weight.
9. Any user with Toxic can do the same as Toxic Spikes do, and more if they predict it's switch in, a good move to have between your special sweepers, because it doesn't only cripple Chansey.
10. Any special sweeper or physical attacker that can deal 50%+ of damage to Chansey can make her thing twice before switch-in, or even if she does switch-in when you din't attacke, Chansey will just paralize you and switch, leaving you with a free setup turn, and a free attack to the switch-in, and if Chansey remains, you can just make her healing herself on every turn until you drain it's PP, if you're with a bit of lucky of not being full paralized more than 3 times.
11. Lum Berry is a good option if you want to check Chansey and actually any Thunder Wave and Sleep Powder user. Just setup or attack right away, and if you can deal her 34% or more of damage, then you can bypass it's Thunder Wave and K.O her or force it to switch-out. Less raw power is needed depending of the hazards on the field. 30%+ with SR on the field, less 2% of each layer of spikes, less 8% with one layer of Toxic Spikes, 6% with two layers. On the worst scenary, you can still beat her with 25%+ of damage per attack (less factoring hazards) and just face to being paralized, not a so-bad problem if your special attacker is slow or if you have a cleric.
12. Sleep Clause to her, total spell doom to the blob.
13. Ghost Types with substitute or 101HP substitute users, they can also setup on her face, too.
14. Safeguard can mantain safe your special sweepers from her as long they can setup Calm Mind or Nasty Plot to bypass the defense of the blob.
15. Any STAB-Figthing move checks her. And any strong Fighthing Move on decent users, too.
16. Pressure users can overstall her without any major problem and on any moment, if you're using one.
17. Hitmonlee. (With Limber)
18. Slow Guts users can actually use it's Thunder Wave for good. Any user with Toxic or Flame Orb doesn't fear nothing from Chansey, too.
19. Gothorita trap with Rest. Wynaut trap.
20. Trapping moves alone usually works, too, and more if she's trying to wish pass.
So, Chansey can be used as setup fodder by a good number of threats, Chansey can be dealed or beated by a good, good number of support moves, Chansey have huges problems against Sleep and Toxic (actually, more from Toxic Spikes, and Sleep if used by what it's trying her to check), and doesn't enjoy paralize, too. Chansey can be trapped. Chansey can be overstalled. Chansey can be bypassed by a good number of special attackers with the correct moves or items. Chansey doesn't any surprise factor at all. The cleric variant is easier to handle because she can't pass titanic wishes, so, she's prone to being dead weight without any major trouble. Toxic variants are even easier to handle, but they will reduce your time of sweeping, but you can still sweep with it if you have the correct moves, anyway.
Not counting the obvious posibility of hax by doing critical-hits, freezing it with your special sweeper, special defense reduction, and all that stuff, not relevant at all. Of course not all the metods works with all of the sets, but the majority works at some degree with all the sets, and if you can't handle any, but any way of those wallbreaking metods on your team, then Chansey is not your unique problem.
