Determining the unreacted equation of state of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) is challenging because it exhibits low crystal symmetry and low X-ray scattering strength. Here, we present the first high-pressure single-crystal X-ray diffraction (SXD) study of this material. Our SXD results reveal a previously unknown transition to a monoclinic phase above 4 GPa. No abrupt change of the volume occurs but the compressibility changes. Concomitant first principles evolutionary crystal structure prediction USPEX calculations confirm this transition and show that it involves a pressure-induced in-plane shift of the layers of TATB molecules with respect to the ambient-pressure phase.