I pour some laquer thinner in a wide, flat old aluminum frying pan I kept for such things [flat so it doesn't require a lot of the thinner]. Soak the chain, push it around with a stick or old toothbrush. Same set-up works for my table saw blades, with some brushing involved.
My airplane mechanic buddy uses Simple Green, a version which says "Aviation" above the "Simple Green" name. I asked him what the difference is, he said it is formulated to be safe if the overspray hits anything plastic [like airplane windows]. I wasn't aware Simple Green was damaging to plastic, but I've never used it anyway. But I am going to check into this stuff. Haven't gotten around to asking him where he gets it [owning a shop, he probably gets it from some aviation supplies place]...we were interrupted the other day when I was reading the label on the bottle in his hangar. Someone else here probably has info' on the stuff...I've seen numerous references to Simple Green on this forum.