Watch the Chicken Pickin': Solo 2 online guitar lesson by Joe Dalton from Big Twang
The solos sometimes have a rapid succession of notes. Very often there are flashy licks strung together by rapid scalar passages. Quoting the melody is rare. In this sense, you can compare a chicken pickin' solo to bebop.
Listen to Albert Lee on Albert's "Country Boy" or Emmy Lou Harris' "Luxury Liner", Arlen Roth on Arlen's "Rooster", Ray Flacke on Ricky Scaggs "One Way Rider" or "Highway 40 Blues", and Brent Mason on his Hot Wired album and various Alan Jackson cuts.