I have had something similar, it turned out to be the endmill, switched to another of a different brand and the chatter went away.
An ever so slight bit of pullout will cause this too, the flange of the holder needs to be seated well against the spindle nose.
Using the shortest endmill possible for the job helps as well.
My main endmill is .250, it causes the least of problems, smaller is good as well, the larger ones are more "finicy"
The Z jibsk have a bearing on this as well.
once chatter is introduced its hard to get rid of it, kind of a self sustaining thing.
I made mainly stainless parts and fittings on my lathe and Bridgeport, a few years of that gives plenty of experience with chatter ha!
I have an 1100 s3 so its a similar size machine.