The crystal chemistry of a new structure type found in the Pb−M−B−O system, PbMBO4 (M = Al, Ga), was extended to include M = Cr, Mn, and Fe. Extension to other trivalent ions, such as Ti, V, Co, Sc, In, and Y, failed for various reasons. Single crystals were grown from a PbO flux for M = Mn and Fe and the crystal structures were solved from X-ray single-crystal diffraction data. For M = Cr, the structure was refined from neutron powder diffraction data. The crystal structure is described in Pnma and features chains of edge-sharing MO6 octahedra extended along the b-axis. Rigid, planar BO3 groups bridge the MO6 octahedra both within and between the chains, forcing the two M−O−M bridging angles involved in the shared edge to be highly asymmetric and constraining the M−M distances to be roughly constant at 2.97 Å. In all cases, one-dimensional short-range magnetic correlations were observed in the magnetic susceptibility data which were antiferromagnetic for M = Cr and Fe and ferromagnetic for M = Mn. Values for the intrachain exchange, J/k B, were extracted from fits to standard models and were −4, −26, and +11 K for M = Cr, Fe, and Mn, respectively. Long-range order was observed below 8.3, 31, and 125 K for M = Cr, Mn, and Fe, respectively, and magnetic structures were refined from neutron powder diffraction data. PbCrBO4 and PbFeBO4 both show antiferromagnetic long-range order with the b-axis antiferromagnetic chains coupled ferromagnetically, while for PbMnBO4 both intra- and interchain couplings are ferromagnetic. Thus, this latter material is a rare example of a ferromagnetic insulator. Attempts to rationalize the observed intrachain J/k B values by reference to magneto-structural correlations were largely unsuccessful due to a lack of appropriate model compounds.