Idle is the enemy during chainsaw break-in.
Follow the manual, but the key is to run it under varying loads and avoid prolonged idling.
Most manufacturers recommend a break-in period of about 3-5 tanks of fuel, during which you should vary the RPMs constantly. Don’t let it sit and idle for more than a few seconds — the rings need pressure to seat properly against the cylinder walls. That means actually cutting, not just revving in the air.
Also, run the fuel mix slightly richer if your saw has adjustable carburetor screws. Lean mixtures run hot and can damage a fresh engine. Let the saw cool fully between tanks — heat cycling helps the parts get acquainted without warping.
Once you’re through the first few tanks, recheck the chain tension and the air filter. Then treat it like any other saw.
Future you will thank present you for taking the hour to do it right.