A compact cold atom beam source based on a multistage two-dimensional magneto-optical trap (MOT) has been demonstrated and characterized. The multiple-stage design greatly reduces the overall size of the source apparatus while providing a high flux of atoms. The cold atom beam was used to load a separate MOT in ultrahigh vacuum, and we obtained an actual trap loading rate of 1.5 x 109 atoms/s while using only 20 mW of total laser power for the source. The entire source apparatus, including optics, can fit into a 4 cm x 4 cm x 13 cm volume.