Perplexing Chimera is a staple in a couple of EDH decks, but what makes it so good?
The most obvious use for this card is to keep this card on the board until your opponent plays something awesome. In Limited, that would be your opponent's bomb. It doesn't even have to be a creature, as it can be any spell. Of course, if this card is on the field, it would prevent your opponent from playing said bomb. Then again, if the opponent gains control of this card, they can then use its effect to your detriment, as well. Deployed correctly, though, especially in Limited, this card is a game changer. A 3/3 for 4U (4 colorless, one Blue) is nothing special, really. If you don't plan on playing anything too spicy after giving your opponent this, you've likely won the game.
The best home for Perplexing Chimera, however, is in Commander! In particular, there's Zedruu the Greathearted. The kind-hearted and generous Minotaur Monk relies on giving opponents cards that they don't want in exchange for cards they really don't want to lose. With Zedruu, you'd gain a life and draw a card at the beginning of your upkeep as long as this is under someone else's control. Still, you'd have to be careful, because that opponent may steal one of your things in return. But then, you could later steal one of their things, as well! Best of all, there's a card in Commander called Homeward Path that allows you to regain control of permanents you own. There are other cards that do that, but Homeward Path is a simple colorless land that would allow you to abuse this card over and over again. The Chimera can become a maddening little troll in a Zedruu deck.
But Zedruu is not the only Commander that has use for the Perplexing Chimera's ability. Roon of the Hidden Realm likes to make things go away and come back. How does this benefit you exactly when it comes to the Chimera? Well, you can, for one thing, get your Chimera back with his ability. Roon's ability can target creature's on your opponent's side of the board, not just your own. Because that creature comes back under its owner's control, you get to not only keep your opponent's thing, but your Chimera, as well. Good stuff. The Chimera pops up in a few other Commander decks, as well, probably for the fun of it.
While the Perplexing Chimera never really saw competitive Constructed play, the effect is pretty bonkers when you really sit there and consider it. With decks that rely on a few specific spells for a win condition, the Chimera can ruin their day. There was a time that I could actually see this side-boarded in for certain match-ups in Eternal formats such as Legacy and Vintage. Maybe I was overthinking its usefulness in those high-power formats.
However, Perplexing Chimera did see a bit of play in Theros Block Constructed in Magic Online, as seen in this mono-blue deck in the sideboard. It was also seen as a two-of in the sideboard of this Devotion to Blue Standard deck that placed fifth in a Magic Online Premier event. Outside of these two corner cases though, Perplexing Chimera is almost strictly a Commander-only playable card. That's just fine, because it's pretty good at what it does.