Some theorymon:
I don't think Chansey even with Counter will be a huge problem, example vs. Tauros:
Scenario 1:
Tauros uses Leer, Chansey uses TWave / Counter
Chansey uses anything but Reflect, Tauros uses Leer (66% OHKO range already, but one more to be sure / check for Reflect)
Chansey uses anything but Reflect again, Tauros uses Hyper Beam and OHKOs
Scenario 2:
Tauros uses Leer, Chansey uses TWave
Chansey uses Reflect, Tauros uses Leer
Chansey uses anything, Tauros uses Leer
Chansey uses anything, Tauros uses Leer
Chansey uses anything, Tauros uses Hyper Beam and OHKOs
Scenario 2 can be foiled with Tauros FPing or Chansey getting a critical hit, but on the flipside a crit HB from Tauros means Chansey just loses.
vs. Snorlax: With Ice Beam, a freeze war that Chansey has an advantage in, Rest + DE / HB / Submission can fish for a OHKO, Amnesia + Psychic can eventually break it with Spc drops
vs. anything with enough bulk to recover/rest in front of Chansey: Toxic and wait.
Can come up with quite a few more examples, but on paper in a 1v1 scenario Chansey doesn't look broken, even if Toxic wasn't an option.
Some example mons I can think of that can work:
Tauros
-Earthquake / Body Slam
-Blizzard
-Hyper Beam
-Leer
Leer is very important utility in a 1v1 especially for Reflect users, so dropping Body Slam (or Earthquake if you're fine with losing the Gengar matchup) is needed to make room. You only need to get a single Pokemon in Hyper Beam range to win anyway.
Lapras
-Blizzard
-Thunderbolt / Thunder
-Body Slam
-Confuse Ray
Confusion that you can't switch out from, powerful Blizzards with freeze haxing, immunity to freeze haxing, Electric coverage for waters (Thunder is riskier but if it hits, Lapras usually wins over other Waters), paraslam, and lots of bulk. Definitely one of the better mons.
Alakazam
-Psychic
-Reflect
-Thunder Wave
-Recover
Good old fashioned Reflect Zam, an obnoxious pain for anything to break. This I think is possibly more worth looking at than Chansey.
Nidoqueen
-Earthquake
-Blizzard
-Thunder
-Body Slam
All grounds are pretty awful, but if you want to counter Electrics, this is your best bet as it not only beats Zap/Jolt/Raichu/Trode, it has a small chance of haxing past most everything else. No strategy here besides spam attacks, pray for crits in matchups like Lapras or Alakazam, or throw out Blizzards for any matchup a crit can't win for you for a possible freeze-hax win. For Raichu, use Body Slam first, Earthquake will always KO afterwards and paraslam prevents crit Surfs from letting Raichu win.
Edit: Also, no disagreement with any of the bans so far.