DURING its reconnaissance of the asteroid 243 Ida, the Galileo spacecraft returned images of a second object, 1993(243)1 Dactyl1- the first confirmed satellite of an asteroid. Sufficient data were obtained on the motion of Dactyl to determine its orbit as a function of Ida's mass. Here we apply statistical and dynamical arguments to constrain the range of possible orbits, and hence the mass of Ida. Combined with the volume of Ida2, this yields a bulk density of 2.6 +/- 0.5 g cm-3. Allowing for the uncertainty in the porosity of Ida, this density range is consistent with a bulk chon-dritic composition, and argues against some (but not all) classes of meteoritic igneous rock types that have been suggested as compositionally representative of S-type asteroids like Ida.