We trap and cool a gas composed of
40K and
87Rb, using a two-species magneto-optical trap (MOT). This trap represents the first step towards cooling the Bose-Fermi mixture to quantum degeneracy. Laser light for the MOT is derived from laser diodes and amplified with a single high-power semiconductor amplifier chip. The four-color laser system is described, and the single-species and two-species MOTs are characterized. Atom numbers of $1\ifmmode\times\else\texttimes\fi{}{10}^{7}$
40K and $2\ifmmode\times\else\texttimes\fi{}{10}^{9}$
87Rb are trapped in the two-species MOT. Observation of trap loss due to collisions between species is presented and future prospects for the experiment are discussed.