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Chimeras come from Greek mythology, where as far as I know it was just The Chimera. D&D likes to make unique monsters into whole species, and this is what happened here. I remember seeing them statted up for AD&D 2nd Edition in the past, and they’re quite likely much older than that. Here, they’re only on the Monster Manual.
Chimeras in 4e have a lion’s body with a dragon’s wings and tail. Its three heads all sprout from the front: the lion in the middle, a goat to the left, and a dragon to the right. They’re Large Natural Magical Beasts, which means they’re both native to the world and sapient. They speak Common and Draconic but aren’t very smart, at Int 5.
A chimera behaves much like the less cerebral types of dragon: it stakes out territory somewhere and roams the surrounding countriside looking for food to line its stomach and shiny treasure to line its lair. Sometimes other creatures will convince a chimera to work for them as muscle, guards, or mounts. They’re Unaligned, but I guess a peaceful interaction with a chimera would be difficult unless you can convince it you’re not prey.
A chimera is a Level 15 Elite Brute with 366 HP. It has both all-around vision and darkvision, so it can hunt at night just fine and can’t be flanked. It also has Resist 10 fire.
The chimera runs with speed 6, flies with speed 10 (clumsy), and has overland flight 15. Creatures with overland flight can fly at the listed speed outside of combat for extended periods, basically. You can run into a chimera quite far from its lair.
In combat, the chimera will usually attack with all three heads: bites from the lion and dragon, and a gore from the goat (which knocks prone in addition to doing damage). The lion bite is its basic attack, but it can attack with all three heads as a standard action. When it charges it uses the goat head, causing a little more damage than the standing gore attack.
The dragon head can also breathe fire on a close blast 5, targeting Reflex and doing fire damage plus ongoing 10 fire damage (save ends) to anyone it hits. This is an encounter power, but when the chimera is bloodied it will immediately recharge its breath and use it again as a free action. In other words, it works exactly like the breath from a real dragon.
The pictured chimera breathes and resists fire because it has red dragon bits, but they come in all the colors of Tiamat. Just change the element: a black chimera would use and resist acid, a blue one lightning, and so on.
The suggested encounters are both level 15. The first is 2 chimeras and 2 hill giants, and the second a chimera, an azer taskmaster, and 6 azer minion warriors.