In so-called j_eff= 1 / 2 systems, including some iridates and ruthenates, the coherent superposition of t_{2 g} orbitals in the ground state gives rise to hopping processes that strongly depend on the bond geometry. Resonant inelastic X-ray scattering measurements on CaIrO₃ reveal a prototypical j_eff= 1 / 2 pseudospinon continuum, a hallmark of one-dimensional (1D) magnetic systems despite its three-dimensional crystal structure. The experimental spectra compare very well to the calculated magnetic dynamical structure factor of weakly coupled spin-1/2 chains. We attribute the onset of such quasi-1D magnetism to the fundamental difference in the magnetic interactions between the j_eff= 1 / 2 pseudospins along the corner- and edge-sharing bonds in CaIrO₃.