In this paper, the design of a novel chipless ultra-wideband radio-frequency identification (UWB RFID) system is proposed. The system employs printable uniplanar chipless tags and a pair of high-gain reader antennas. The chipless tag is composed of two UWB monopole antennas, connected by a coplanar waveguide (CPW). The tag's ID is represented by a spectral signature in the UWB frequency range, and is created by a multi-resonator embedded on the coplanar waveguide. The detection of the tag's ID is based on using only the amplitude of the spectral signature, which significantly simplifies the complexity of detection. The reader employs two separate Vivaldi antennas - one for transmitting a vertically polarized signal, and the other for receiving a horizontally polarized signal - to reduce the mutual coupling between the uplink and downlink signals. Further reduction of mutual coupling is achieved by using a copper plate at the reader to separate the uplink and downlink signals. These two proposed methods together reduced the mutual coupling by 20 dB. The chipless RFID tag with eight coplanar waveguide resonators in a group and the reader antennas were designed using computer simulation, and fabricated on Rogers substrates for measurement. The results of studies in an anechoic chamber showed that the proposed UWB RFID system could achieve a reading range of larger than 30 cm, at least three times longer than the maximum distance of a similar system reported by others. This indicated that the proposed system has great potential for short-range item tracking at low cost.