Terahertz (THz)-band (0.1-10 THz) communication has been envisioned as a key technology to enable wireless Terabitper-second (Tbps) links. At THz frequencies, the path-loss is governed by the spreading loss and the molecular absorption loss. The latter also determines the available transmission bandwidth, which drastically shrinks with distance. New physical layer solutions that capture this behavior are needed to maximally utilize the THz band. In this paper, the concept of hierarchical bandwidth modulation is introduced for single-transmitter multiple-receiver communication in the THz band. In the proposed modulation scheme, multiple flows of information aimed at users at different distances are transmitted at the same time and over the same frequency, by simultaneously adapting both the modulation order and, more importantly, the symbol time. Details for the modulator and the demodulator implementations are provided. The performance of the proposed modulation is analytically derived, both in terms of the achievable data rate as well as symbol error rate. Extensive numerical results based on analytical channel models that capture the peculiarities of the THz band are provided to illustrate the performance of the proposed scheme. The results show that the proposed modulation scheme can maximize the utilization of the distance-dependent bandwidth of the THz channel, turning molecular absorption into an advantage.