Chrome is a known resource hog. You may want to lower its priority or change Output Plugin used in MediaMonkey.

I don't have any such issue running MM and chrome at the same time.

I do use Google Chrome, but it has serious resource and load balancing issues which on my system causes the introduction of clicks and pops when Media Monkey plays tracks.

It is completely repeatable meaning a track has clicks and pops with Chrome running, and there are no clicks and pops when not, and then click and pops again when Chrome is restarted. Interestingly enough, it doesn't seem to matter which page Chrome is open to, but I have a suspicion that if I open a nasty resource hogging page like Gamespot the clicking would get worse.

It is unlikely to be due to an under-powered PC as it is basically a gaming rig with a good dedicated audio card.