In this paper, the rf-amplitude threshold of chaos in a Josephson junction with quadratic damping is studied. Theoretical predictions based on the method of Melnikov is compared with numerical simulations. It is shown that the chaotic region predicted by the method of Melnikov spans only a narrow region of rf-amplitude and consists of phase locked chaos. The experimentally observed threshold of chaos is shown to coincide with the onset of unlocked chaotic behavior at higher rf-amplitude.