Radar images of near-Earth asteroid 2000 DP107 show that it is composed of an approximately 800-meter-diameter primary and an approximately 300-meter-diameter secondary revolving around their common center of mass. The orbital period of 1.755 +/- 0.007 days and semimajor axis of 2620 +/- 160 meters constrain the total mass of the system to 4.6 +/- 0.5 x 10(11) kilograms and the bulk density of the primary to 1.7 +/- 1.1 grams per cubic centimeter. This system and other binary near-Earth asteroids have spheroidal primaries spinning near the breakup point for strengthless bodies, suggesting that the binaries formed by spin-up and fission, probably as a result of tidal disruption during close planetary encounters. About 16% of near-Earth asteroids larger than 200 meters in diameter may be binary systems.