The orbital parameters of a satellite revolving around 22 Kalliope indicate that the bulk density of this main-belt asteroid is 2.37 +/- 0.4 grams per cubic centimeter. M-type asteroids such as Kalliope are thought to be the disrupted metallic cores of differentiated bodies. The low density indicates that Kalliope cannot be predominantly composed of metal and may be composed of chondritic material with ~30% porosity. The satellite orbit is circular, suggesting that Kalliope and its satellite have different internal structures and tidal dissipation rates. The satellite may be an aggregate of impact ejecta from an earlier collision with Kalliope.