Prominent crater chains on Ganymede and Callisto are most likely the impact scars of comets tidally disrupted by Jupiter and are not secondary crater chains. We have examined the morphology of these chains in detail in order to place constraints on the properties of the comets that formed them and the disruption process. In these chains, intercrater spacing varies by no more than a factor of 2 and the craters within a given chain show almost no deviation from linearity (although the chains themselves are on gently curved small circles). All of these crater chains occur on or very near the Jupiter-facing hemisphere. For a given chain, the estimated masses of the fragments that formed each crater vary by no more than an order of magnitude. The mean fragment masses for all the chains vary by over four orders of magnitude (W. B. McKinnon and P. M. Schenk 1995,Geophys. Res. Lett.13, 1829-1832), however. The mass of the parent comet for each crater chain is not correlated with the number of fragments produced during disruption but is correlated with the mean mass of the fragments produced in a given disruption event. Also, the larger fragments are located near the center of each chain. All of these characteristics are consistent with those predicted by disruption simulations based on the rubble pile cometary nucleus model (in which nuclei are composed on numerous small fragments weakly bound by self-gravity), and with those observed in Comet D/Shoemaker-Levy 9. Similar crater chains have not been found on the other icy satellites, but the impact record of disrupted comets on Callisto and Ganymede indicates that disruption events occur within the Jupiter system roughly once every 200 to 400 years.