A new series of isostructural rare earth compounds R1+xZr1−xNi (R = Er, Tm, Lu; x ~ 0.5) was synthesized from the elements by arc melting and subsequent annealing at 870 K for 1400 h. The crystal structures of the intermetallic compounds were investigated by means of single-crystal X-ray diffraction. They all crystallize in the TiNiSi structure type (space group Pnma, No. 62, oP12). In R1+xZr1−xNi, the R/Zr statistical mixture leading to nonequiatomic compositions occupies the position corresponding to the nickel site of the TiNiSi structure type. The calculated shortest interatomic distances are close to the sums of the single-bond covalent radii of respective elements. Electronic structure calculations performed with the tight-binding LMTO method revealed the non-zero density of states at the Fermi level and suggest metallic character. R1+xZr1−xNi (R = Er, Tm, Lu; x ~ 0.5) undergoes no long-range magnetic ordering down to 2 K.