I recently had an experience that caused me to ask one of our experts off line about chatter. I was tested modules that had previously been "chatterers" before I cut them up for parts and lo and behold, they no longer chattered! I'm of the mind there are two kinds of chatter: One caused by a physical failure of the plastic cam controlling the 110VAC relay and the other caused by some sort of powerline "environment" problem.
I based that conclusion on examining ones that have physically failed and chatter all the time as well as examining units that have no apparent cracks and yet chatter in certain situations. This may start a holy war of sorts because all I have are some miraculously revived chattering appliance modules and no particular theory of operation. Even so, let's try to work this through because it sounds as if your problem correlates with my experience that chatter is not always a physical problem.
Can you swap that module out for others to see if the chatter persists? The two fairly old appliance modules that I've written "Chatters" on *twice* (which means they chattered in their original locations AND when re-tested elsewhere) that are now running the basement lights without issue leading me to conclude that electrical environment is at fault. I realize there might be other issues at play, though. A slightly cracked or worn cam might work mounted horizontally, but not vertically. These units are plugged into grounded circuits now, but they might have been plugged in using a three-wire adapter before when they were chattering. Unfortunately, I did not record that information. I also recall that when they chattered, they were plugged into an outlet strip that had other modules, including a TM751, into the same strip.
Anyway, if you can give us more details about your gear (what type of controller, modules, whether they are modded or not) and what you have that you can swap out we might be able to figure this out. Do you have multiple X-10 RF receiver modules installed? That's something I used to have before that I don't have now which further muddies the waters in terms of running the problem to ground.
-- Bobby G.