High-resolution radar images reveal near-Earth asteroid (66391) 1999 KW4 to be a binary system. The ~1.5-kilometer-diameter primary (Alpha) is an unconsolidated gravitational aggregate with a spin period ~2.8 hours, bulk density ~2 grams per cubic centimeter, porosity ~50%, and an oblate shape dominated by an equatorial ridge at the object's potential-energy minimum. The ~0.5-kilometer secondary (Beta) is elongated and probably is denser than Alpha. Its average orbit about Alpha is circular with a radius ~2.5 kilometers and period ~17.4 hours, and its average rotation is synchronous with the long axis pointed toward Alpha, but librational departures from that orientation are evident. Exotic physical and dynamical properties may be common among near-Earth binaries.