Pierce Brosnan, Remington Steele, references a 1968 Steve McQueen movie called The Thomas Crown affair. He would later go on to star in the remake of the same film, by the same name.
Steele adopts the persona of John Robie, Cary Grant's character in To Catch A Thief (1955).
"Chomping at the bit" is a bowdlerization of "champing at the bit", which is the original euphemism for being impatient, being that it comes from horses champing at their bits. Champ means to mash or make mashing or gnashing movements. Whether it was originally misspelled or simply that champing was never widely understood outside of horse racing or rural settings, chomping has become the more common usage, albeit inaccurate.