Polar and chiral crystal symmetries confer a variety of potentially useful functionalities upon solids by coupling otherwise noninteracting mechanical, electronic, optical, and magnetic degrees of freedom. We describe two phases of the 3D perovskite, CsSnBr₃, which emerge below 85 K due to the formation of Sn(II) lone pairs and their interaction with extant octahedral tilts. Phase II (77 K < T < 85 K, space group P2₁/m) exhibits ferroaxial order driven by a noncollinear pattern of lone pair-driven distortions within the plane normal to the unique octahedral tilt axis, preserving the inversion symmetry observed at higher temperatures. Phase I (T < 77 K, space group P2₁) additionally exhibits ferroelectric order due to distortions along the unique tilt axis, breaking both inversion and mirror symmetries. This polar and chiral phase exhibits second harmonic generation from the bulk and pronounced electrostriction and negative thermal expansion along the polar axis (Q₂₂ ≈ 1.1 m⁴ C^-2; α_b = −7.8 × 10^-5 K^-1) through the onset of polarization. The structures of phases I and II were predicted by recursively following harmonic phonon instabilities to generate a tree of candidate structures and subsequently corroborated by synchrotron X-ray powder diffraction and polarized Raman and ⁸¹Br nuclear quadrupole resonance spectroscopies. Preliminary attempts to suppress unintentional hole doping to allow for ferroelectric switching are described. Together, the polar symmetry, small band gap, large spin-orbit splitting of Sn 5p orbitals, and predicted strain sensitivity of the symmetry-breaking distortions suggest bulk samples and epitaxial films of CsSnBr₃ or its neighboring solid solutions as candidates for bulk Rashba effects.