One of the main reasons I have found for chattering of a safety valve is improper line sizing.  Specifically, the inlet line to the safety valve.  What's happening is if the system sees an overpressure the safety valve opens (fully, assumes a true safety valve with huddling chamber).  The valve will remain open as long as it is at app. 90% full capacity.  If the line sizing restricts this flow the valve closes.  Pressure builds, it opens fully.  The process is cyclic and the rapid opening/closing prematurely wears down the valve nozzle and seat.
The valve pops on static pressure increase, the flow losses cause it to reseat before the system pressure (at the source has cleared) and the cycle repeats...
look for reducers, excessive bends and elbows, and valving in the inlet line. also look for long piping runs beteen the relief valve and the vessel or the pipe being protected.
usually once the piping loos during full lift are identified, the reason for chatter is obvious.

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