>>33249368Chansey (Level 100, perfect DVs and stat exp.)
HP: 703
Attack: 108
Defense: 108
Speed: 198
Special: 308
Mewtwo (Level 100, perfect DVs and stat exp.)
HP: 415
Attack: 318
Defense: 278
Speed: 358
Special: 406
Chansey may not be able to outspeed Mewtwo, but in a 1v1 battle, it may be able to get in Light Screen, Substitute, Toxic, and Soft-Boiled. Mewtwo with Psychic would do 129-152 damage on the first turn (no Special boosts), or 250-294 damage if it got a critical. Chansey's substitute would have 177 HP, and after Light Screen, Mewtwo's Psychic would only do 66-77 damage (critical hits ignore Light Screen in Gen I).
Turn 1
Mewtwo used Psychic!
Chansey (703 > 551)
Chansey used Light Screen!
Turn 2 (Light Screen turn 1)
Mewtwo used Psychic!
Chansey (551 > 474)
Chansey used Toxic! Mewtwo was badly poisoned!
Mewtwo (415 > 389)
Turn 3 (Light Screen turn 2)
Mewtwo used Psychic!
Chansey (551 > 397)
Chansey used Substitute!
Chansey (397 > 221), Substitute (177)
Mewtwo (389 > 337)
Turn 4 (Light Screen turn 3)
Mewtwo used Psychic!
Substitute (177 > 100)
Chansey used Soft-Boiled!
Chansey (221 > 572)
Mewtwo (337 > 259)
Turn 5 (Light Screen turn 4)
Mewtwo used Psychic!
Substitute (100 > 23)
Chansey used Soft-Boiled!
Chansey (572 > 703)
Mewtwo (259 > 155)
Turn 6 (Light Screen turn 5)
Mewtwo used Recover!
Mewtwo (155 > 362)
Chansey used irrelevant move!
Mewtwo (362 > 232)
Light Screen faded!
Turn 7
Mewtwo used Psychic!
Substitute (23 > 0)
Chansey used Light Screen!
Mewtwo (232 > 76)
And it's obvious at this point that it's hopeless for Mewtwo. This isn't taking criticals into account, but it is assuming that Mewtwo is getting really lucky and doing 100% damage with each hit instead of as low as 85% going by the random factor. A physical Mewtwo might make a difference, but then it's not getting STAB, and the only move that does more than STAB Psychic on Mewtwo that isn't Self-Destruct is Hyper Beam, which always has a cooldown period.