Did it arise from a mixture of chattering and murmuring?
It seems to come from Yorkshire dialect, with direct meaning of mutter.
Also, to me the connection with 'chant' looks interesting:
late 14c., from O.Fr. chanter "to sing, celebrate" (12c.), from L. cantare, frequentative of canere "sing," from PIE base *kan- "to sing" (cf. Gk. eikanos "cock," O.E. hana "cock," both lit. "bird who sings for sunrise;" O.Ir. caniaid "sings," Welsh canu "sing"). The frequentative quality of the word was no longer felt in Latin, and by the time French emerged the word had entirely displaced canere. Related: Chanted; chanting. The noun is recorded from 1670s, from Fr., from L. cantus, from pp. stem of canere. — Etymonline
I would hazard a guess at a modification of chant, which according to Etymonline appeared in the 1600's from the French chanter.
According to Dictionary.com, its origin is from:
1590–1600; orig. dial. (Midlands, N England) chunter, chunder, chunner; — Random House
Interesting to know that the Scottish have a similar word "channer". However, the origin of both words were deemed:
probably of imitative origin — Collins
I reckon the origin of the word was a result of onomatopoeia. The way "bow-wow" or "meow" were originated from imitating the sounds of dogs and cats, "chunter" was probably imitating murmuring sounds.