The most-common reason for chatter is voltage drop.
If the motor draws excessive starting current, or the power supply isn't stiff enough, the voltage at the motor-starting relay can drop to the point where the relay lets go. When the relay switches the motor off, the voltage recovers and the relay can pull in again. Then the voltage drops again ...
It's easy enough to diagnose -- just measure the voltage on the motor-starting relay. You'll need something that can detect transients, either a voltmeter with a fast update rate, with a min-max function, or an analog voltmeter. If the voltage drop is severe enough to let the relay let go, an incandescent lightbulb will probably tell you what you need to know.