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Ferroaxial order is a relatively underexplored phenomenon that is characterized by a rotational structural distortion with an axial vector symmetry. The symmetry requirement for a ferroaxial transition is broken mirror symmetry in a plane parallel to the rotation axis. Ferroaxial order when coupled with ferroelectric order — that is characterized by the breaking of inversion symmetry — can lead to ferrochiral materials that combine chirality with electric polarization. Ferrochiral materials are rare. Here, we report direct observation of a strain-induced ferrochiral transition in a single crystal of a quasi-one-dimensional chalcogenide, BaTiS₃. Using a combination of aberration-corrected scanning transmission electron microscope (STEM) imaging and density-functional-theory (DFT) calculations, we show that biaxial strain along ab-plane perpendicular to the 1D chains of TiS₆ octahedra in BaTiS₃ transforms it from a higher symmetry phase with P6₃cm space group to a ferrochiral P6₃ phase. The ferrochiral phase is characterized by a rotational distortion of the TiS₆ octahedra along the axis containing the chains, and polarization along the chain direction. We also show direct observation of the ferrochiral domains and domain walls with atomic resolution. Finally, using phenomenological modeling, we propose that the chirality can be switched with an external electric field.