The neutron-rich nucleus Ba144 (t1/2=11.5 s) is expected to exhibit some of the strongest octupole correlations among nuclei with mass numbers A less than 200. Until now, indirect evidence for such strong correlations has been inferred from observations such as enhanced E1 transitions and interleaving positive- and negative-parity levels in the ground-state band. In this experiment, the octupole strength was measured directly by sub-barrier, multistep Coulomb excitation of a post-accelerated 650-MeV Ba144 beam on a 1.0−mg/cm2 Pb208 target. The measured value of the matrix element, ⟨31−∥M(E3)∥01+⟩=0.65(+17−23) eb3/2, corresponds to a reduced B(E3) transition probability of 48(+25−34) W.u. This result represents an unambiguous determination of the octupole collectivity, is larger than any available theoretical prediction, and is consistent with octupole deformation.