In this paper, the performance of indoor Terahertz (THz) communication systems with one-bit digital-to-analog converters (DACs) is investigated. Array-of-subarrays architecture is assumed for the antennas at the access points, where each RF chain uniquely activates a disjoint subset of antennas, each of which is connected to an exclusive phase shifter. Hybrid precoding, including maximum ratio transmission (MRT) and zero-forcing (ZF) precoding, is considered. The best beamsteering direction for the phase shifter in the large subarray antenna regime is first proved to be the direction of the line-of-sight (LOS) path. Subsequently, the closed-form expression of the lower-bound of the achievable rate in the large subarray antenna regime is derived, which is the same for both MRT and ZF and is independent of the transmit power. Numerical results validating the analysis are provided as well.