The first problem is that the chain isn't harder then the armor, most chains are steel, but unlikely to be as hardened as forged and heat treated plate armor of that period. So what would actually happen is that you'd press the chainsaw to the armor and it would pretty much immediately be blunted, ruining it's ablity to actually cut anything let alone digging further into the metal.
Chainsaws for cutting metal exist, but these are industrial models with carbide or even diamond studded chains to get the needed overmatch in hardness to cut common metals, and even then they usually require an external liquid hookup to continuously dose the work surface to keep from frying themselves with friction heating. The second issue is it isn't anything like a quick slash through a tree limb, it takes an extended period of carefully controlled cutting to get through any significant amount of metal.
That control is the third issue, the saw needs to be kept on the same spot and advanced carefully, without excessive side loads. Between the target moving the arm, the arm/armor being curved, and how difficult it would be for the attacker to actually keep the saw steady when slashing it's very, very unlikely you'd be able to get the blade to bit in, even if it had the theoretical hardness needed it would just keep skittering along the surface.
Finally even if it did slightly dig in somehow any sort of yanking side force could probably pretty easily rip the chain off the bar and stop the saw.
Every now and then I get a reminder of why I love Danbooru.
