The compound Pb3Bi2S6 is investigated by X-ray diffraction on single crystals in a diamond-anvil cell between 0.0001 and 10.5 GPa. It undergoes a first-order phase transition at hydrostatic pressure between 3.7 and 4.9 GPa. The space group symmetry changes from Bbmm to Pbnm, and the unit-cell volume decreases by 4%. The transition is strongly anisotropic, with a contraction along one of the crystal axes by 16% and expansion along another one by 14%. This is a piezoplastic phase transition, a displacive pressure-induced phase transition with systematic shearing of atomic planes and a migration of chemical bonds in the structure. In the case of Pb3Bi2S6 the transition is achieved by the change of the archetypal architecture of the structure-building modules from a PbS-like to a SnS-like arrangement and a loss of mirror planes on the contact surfaces of modules. The phase transition is reversible with a preservation of the single crystal, which is a result of the stereochemical influence and migration of the S-2 lone electron pairs of Pb-II and Bi-III.