Alteration from べちゃくちゃ (bechakucha), an onomatopoeia for a large number of people talking noisily. The shift from initial /b/ to /p/ changes the meaning from an emphasis on noisy to an emphasis on lively. Compare English gabble, chatter, yackety-yak.
Also analyzable as a compound of root elements:
- ぺちゃ (pecha): onomatopoeia for lively talking, evocative of the sound of lips and tongues smacking; also onomatopoeia for the sound of water splashing against something.
- くちゃ (kucha): onomatopoeia for the sound of paper crumpling; by extension, indicates that something is being done in a confused or disorganized fashion.