Recent advances(1-5) in the magnetic trapping and evaporative cooling of atoms to nanokelvin temperatures have opened important areas of research, such as Bose-Einstein condensation and ultracold atomic collisions. Similarly, the ability to trap and cool molecules should facilitate the study of ultracold molecular physics and collisions(6); improvements in molecular spectroscopy could be anticipated. Also, ultracold molecules could aid the search for electric dipole moments of elementary particles(7). But although laser cooling (in the case of alkali metals(1,8,9)) and cryogenic surface thermalization (in the case of hydrogen(10,11)) are currently used to cool some atoms sufficiently to permit their loading into magnetic trays, such techniques are not applicable to molecules, because of the latter＇s complex internal energy-level structure. (Indeed, most atoms have resisted trapping by these techniques.) We have reported a more general loading technique(12) based on elastic collisions with a cold buffer gas, and have used it to trap atomic chromium and europium(13,14). Here we apply this technique to magnetically trap a molecular species-calcium monohydride (CaH). We use Zeeman spectroscopy to determine the number of trapped molecules and their temperature, and set upper bounds on the cross-sectional areas of collisional relaxation processes. The technique should he applicable to many paramagnetic molecules and atoms.