We present the first simultaneous trapping of two different ultracold atomic species in a conservative trap. Lithium and cesium atoms are stored in an optical dipole trap formed by the focus of a CO₂ laser. Techniques for loading both species of atoms are discussed and observations of elastic and inelastic collisions between the two species are presented. A model for sympathetic cooling of two species with strongly different mass in the presence of slow evaporation is developed. From the observed Cs-induced evaporation of Li atoms we estimate a cross-section for cold elastic Li-Cs collisions.