Spin-frustrated chains of Cr-3 triangles are found in the new metal boride TiCrIr2B2 by synergistic experimental and theoretical investigations. Although magnetic ordering is found at 275 K, competing ferro- and anti-ferromagnetic interactions coupled with spin frustration induce a rather small total magnetic moment (0.05 mu(B) at 5 T), and density functional theory (DFT) calculations propose a canted, nonlinear magnetic ground-state ordering in the new phase. TiCrIr2B2 crystallizes in the hexagonal Ti1+xOs2-xRuB2 structure type (space group P (6) over bar 2m, No. 189, Pearson symbol hP18). The structure contains trigonal planar B-4 boron fragments with B-B distances of 1.76(3) angstrom alternating along the c-direction with Cr-3 triangles with intra- and intertriangle Cr-Cr distances of 2.642(9) and 3.185(1) angstrom, respectively. Magnetization measurements of TiCrIr2B2 reveal ferrimagnetic behavior and a large, negative Weiss constant of -750 K. DFT calculations demonstrate a strong site preference of Cr for the triangle sites, as well as magnetic frustration due to indirect anti-ferromagnetic interactions within the Cr-3 triangles.