In this paper, a three-dimensional (3-D) ultra-wideband time-of-arrival localization scheme that employs a single cluster of receivers is studied. The receivers are placed on a two-dimensional plane within a few decimeters, and no wireless synchronization is required among the receivers. The optimum 3-D receiver placement is analyzed in the sense of minimum estimation variance defined by the Cramér-Rao lower bound. The position error bound as a function of the number of receivers and the distance between the source and the receiver unit is derived. An average position estimation error of 26.6 cm is achieved in experiments when the transmitter is within 10 meters of the receiver unit, where four receivers are placed in the same place within a circle of radius 50 cm.