What kind of lathe are you using? Can you run backwards without causing the chuck to unscrew? Or, can you hold the workpiece in a collet?
Anyway, what I discovered in my long saga with chattering cutoff tools is that one big danger is self-feeding of tool into work. A very rigid machine limits this, but not all machines are all that rigid. One alternative is to turn the tool upsidedown and spin the work backwards, so the cutting forces instead tend to pull the tool out of the work. This will prevent grabbing due to self-feeding.
The other issue is to shape the cutting tool so it's max width at the cutting edge and tapers as one goes away from the cutting edge. In other words, the tool becomes slightly necked, prevent cutting on the sidewalls of the groove. Make sure that everything is square and locked, so the tool feeds straight into the groove without translating into either sidewall.
And ensure that the groove is flooded with cutting fluid. A brush will not do.
Now, I'm assuming that your lathe is tight. If not (and my lathe was not tight at first), you must first fix the lathe. I must say one stark moment was when I found that I couldn't make a 0.0625" wide slot in mild steel using my 1500# lathe. I knew that this cannot be right, and started the investigation. Everything that could be loose was loose. Search past RCM postings for "Clausing 5914 chatter" and "Trepanning and Parting Off" in the subject for the long sad saga.