A battery powered chain saw is one way to go. Another is a corded electric chain saw like DE has already considered.
My preference is a corded, because I absolutely LOATH lithium batteries. Three year life-max. The charges are extremely expensive, and MUST be matched to the single appliance that you have due to the DIGITAL CIRCUITRY match (controlled by DIGITAL-itis built into the battrty *prevents the damn things from exploding and can also contain 'lifetime' deactivation coding for the battery also - like many inkjet cartridges.)
Long cords ? Yeah, but not needed. You can build a portable lead-acid battery pack with 110volt inverter mounted to a portable hand cart for $100-135 dollars.
Get a 650 VA car battery (longer lifetime than ANY lithium batteries, chargers interchangeable for all 12v batteries, and completely rebuildable/recyclable -unlike lithium bats.) Inverters available at any car parts store/camper stores - 10-15 Amp - for less than $50. Battery - 650VA around $50 @Walmart, hand carts around $35 - pneumatic wheels of course and add a bracket to hang the saw on. Assume you already have a charger for car batteries.
This would be heavy, but with those wheels on it, it would be easy to haul it around the forest, and not as tiring as even carrying the chain saw. Voila - no mile long cords needed.
Another thing about lithiums - if you ever completely drain one to an absolute NO CHARGE level - you will never be able to recharge it again. Another built in 'safety feature'. So don't store one that is at a low charge level for extended periods of time or it will be DOA eternally. Not so with the good ole lead acids - which hold a whole hell of a lot more 'punch' per pound than any other battery - including ALL lithiums.
Expensive ? Nope - not in long run. Replace one of those lithium packs for a saw, or buy a new charger because the digital electronics fried and you easily FAR exceed the cost of the above contraption.
Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good ...
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