The octupole strength present in the neutron-rich, radiocative nucleus $^{146}$Ba has been experimentally determined for the first time using Coulomb excitation. To achieve this, $A$=146 fission fragments from CARIBU were post-accelerated by the Argonne Tandem Linac Accelerator System (ATLAS) and impinged on a thin $^{208}$Pb target. Using the GRETINA $\gamma$-ray spectrometer and the CHICO2 heavy-ion counter, the reduced transition probability $B(E3;3^-$$\rightarrow$$0^+)$ was determined as 48($^{+21}_{-29}$) W.u. The new result provides further experimental evidence for the presence of a region of octupole deformation surrounding the neutron-rich barium isotopes.