Millimeter-wave communications rely on beamforming gain from both transmitters and receivers to compensate for severe propagation loss. To achieve adequate gain, beam training is required to identify propagation directions. The main challenge in beam training arises from maintaining low overhead with increased array size. This paper presents a novel one-shot beam training technique that utilizes the emerging architecture of true-time-delay (TTD) arrays. We first show that TTD arrays facilitate frequency dependent beam steering. The proposed training procedure with TTD arrays then exploits this fact by using a single radio-frequency-chain to multiplex different subcarriers into different sounding directions. We derive conditions on the parameters of TTD array configuration and physical layer to achieve scanning of the entire angular domain with a single orthogonal frequency-division multiplexing (OFDM) training symbol. The estimation of propagation directions with high resolution is achieved via low-complexity digital signal processing of spatially coded subcarriers. Simulation results show that this TTD array based approach requires an order-of-magnitude fewer training symbols than those of phased arrays.