One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and emergent phenomena. The spin-1/2 Heisenberg chain with antiferromagnetic nearest neighbour interactions is an important reference system; its elementary magnetic excitations are spin-1/2 quasiparticles called spinons that are created in even numbers. However, while the excitation continuum associated with two-spinon states is routinely observed, the study of four-spinon and higher multi-spinon states is an open area of research. Here we show that four-spinon excitations can be accessed directly in Sr₂CuO₃ using resonant inelastic x-ray scattering (RIXS) in a region of phase space clearly separated from the two-spinon continuum. Our finding is made possible by the fundamental differences in the correlation function probed by RIXS in comparison to other probes. This advance holds promise as a tool in the search for novel quantum states and quantum spin liquids.