It’s because the 'ch is a shortened ‘eich’.
In full - Chaethoch chi mo eich dihuno (lit. you didn’t have your waking), but eich shortens to 'ch after the o.
In the singular,
In full - Ches i mo fy newis (lit. I didn’t have my choosing), but in speech the ‘fy’ has fallen away but leaving the mutation it causes - newis is the nasal mutation of dewis.