A new series of tetragonal LaPtSi-type mixed-anion arsenides, LaMAsHx (M = Co, Ni, or Cu), has been synthesized using high-temperature and high-pressure techniques. The crystal structure of these intermetallic compounds determined via powder neutron diffraction is composed of a 3D framework of three connected planes with the La ions filling the cavities in the structure. Each late transition-metal ion M, all of which have relatively large electronegativities, behaves like a main group element and forms a planar coordination configuration with three As ions. The trigonal-bipyramidal coordination adopted by the H in the cavity, HM2La3, is compressed along the C-3 axis, and unusual M-H chains run along the x and y directions, reinforcing the covalent framework. These chains, which are unique in solids, are stabilized by covalent interactions between the M(4)s and H 1s orbitals.