At least part of his inspiration is Tonight Show host Jay Leno who is also known for his large chin. He voices the Crimson Chin in his second appearance (first in the main series) onward.
The Crimson Chin was inspired by a number of other comic characters, including Batman and Superman. The Tick may have played a very important role, as The Crimson Chin's suit and large jaw may have been inspired by The Tick.
Crimson Chin's Danish name is Hagemanden meaning "The Chin-man", is a reference to Superman.
According to The Masked Magician, the Crimson Chin unintentionally created his archnemesis The Bronze Kneecap by accidentally tripping the latter with his large chin while they were participating in a Jai Alai game, causing Ron Hambone to lose the said game (had that not happened Hambone would have won as he only needed one more point to win the game). Hambone wanted revenge on the Chin mainly because the Chin did not apologize for purposely tripping him. As of now he still apparently will not say to the Kneecap that he was sorry for the incident.
In older episodes, he would occasionally be seen wearing a cape that appears out of nowhere and only when he is given a far off shot.
In the Swedish dub, the character's name is "Rödhakan", translating to "The Red Chin" in Swedish.
In Abra-Catastrophe, the photo shows him under "The Crimson Chimp" (pictured) when Earth got ruled by apes and Dimmsdale becomes Chimpsdale.