Prompted by this post, I leveled up a Ledian until it got Mach Punch, then caught a male Smeargle in the friend safari that had sketched Mach Punch. I bred it and a female Chesnaught together. The Chespin egg was born with Tackle and Grol. Chespin does not learn Mach Punch via egg move.Then it should be able to from the Chimchar line, which has access to Mach Punch and is in the Field Group, not to mention they are both starters + fighting-types, seems very likely to me.
I can add the following to that list as moves that Chespin does not get:Did some breeding for egg moves with no luck. Chespin does not get the following as egg moves:
Double Kick, Rototiller (Diggersby)
Work Up, Noble Roar (Litleo)
Circle Throw, Vital Throw, Arm Thrust (Pancham)
Sucker Punch, Cotton Guard (Furfrou)
Baton Pass, Morning Sun, Moonlight, Yawn (Espeon & Umbreon)
Zen Headbutt (Psyduck)
Revenge, Pursuit, Crush Claw, Embargo (Zangoose)
Rapid Spin, Body Slam, Iron Defense (Torkoal)
Low Kick, Hi Jump Kick, Focus Punch, Payback (Scraggy)
Force Palm, Reversal, Close Combat (Lucario)
Stealth Rock, Toxic Spikes, Sacred Sword, Stun Spore (Smeargle)
Focus Energy (Nidorino)
Confirming.I got a Chespin with Belly Drum via wonder trade, so it must get it from Chesnaught with breeding.