Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d^{8.67}) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-T_{c} superconductivity. One such material, La_{4}Ni_{3}O_{8}, undergoes a semiconductor-insulator transition at ∼105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies the formation of spin stripes akin to single layer nickelates. Here we report single crystal neutron diffraction measurements (both polarized and unpolarized) that establish that the ground state is indeed magnetic. The ordering is modeled as antiferromagnetic spin stripes that are commensurate with the charge stripes, the magnetic ordering occurring in individual trilayers that are essentially uncorrelated along the crystallographic c axis. A comparison of the charge and spin stripe order parameters reveals that, in contrast to single-layer nickelates such as La_{2-x}Sr_{x}NiO_{4} as well as related quasi-2D oxides including manganites, cobaltates, and cuprates, these orders uniquely appear simultaneously, thus demonstrating a stronger coupling between spin and charge than in these related low-dimensional correlated oxides.