Catalyzes the conversion of O-acetylserine (OAS) to cysteine through the elimination of acetate and addition of hydrogen sulfide. hydrogen sulfide + O-acetyl-L-serine = acetate + L-cysteine Competitively inhibited by a four-residue peptide derived from the C-terminus of serine acetyltransferase (CysE). This suggests that CysK1 may associate with CysE in vivo to form a bi-enzyme complex, in which the OASS activity is down-regulated. Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-serine: step 2/2. Homodimer. Belongs to the cysteine synthase/cystathionine beta-synthase family.