Level structures in the neutron-rich ^{144}Ba nucleus have been reinvestigated by measuring prompt γ rays in the spontaneous fission of ^{252}Cf. The previous s=+1 octupole band structure with reflection asymmetric shape has been expanded, and a side quadrupole band structure based on a 3^{+} state with reflection symmetric shape is identified. Thus, the results show the coexistence of reflection asymmetric and symmetric shapes in ^{144}Ba. This is a first identification of such a shape coexistence structure in a nuclear structure. The other structural characteristics are discussed.