Mark Richter Small Engine Repair does these (or at least did in the past. He's on Rte 25 in Moultonborough, easily found via Google.
Depending on how often you need a chain job, it might over time be worth buying a sharpener and doing them yourself. You can pay a lot for a really good one, or get into one cheap here for $30:
https://www.harborfreight.com/electr...ner-63803.html
The subject has come up many times on another forum, related to wood burning: hearth.com, subforum "The Gear."