High-resolution radar images reveal near-Earth asteroid (66391) 1999 KW4 to be a binary system. The approximately 1.5-kilometer-diameter primary (Alpha) is an unconsolidated gravitational aggregate with a spin period approximately 2.8 hours, bulk density approximately 2 grams per cubic centimeter, porosity approximately 50%, and an oblate shape dominated by an equatorial ridge at the object's potential-energy minimum. The approximately 0.5-kilometer secondary (Beta) is elongated and probably is denser than Alpha. Its average orbit about Alpha is circular with a radius approximately 2.5 kilometers and period approximately 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.