The F19(γ,n)F18 reaction has been studied by irradiating teflon samples in the X-ray beam of a 25-Mev betatron and detecting the annihilation radiation emitted during the decay of the residual nuclei. The cross section shows maxima at 10.6 (very small), 12.4, 14.0, 16.1, 17.2, and 19.3 Mev. The peak at 12.4 Mev is possibly due to excitation of the last neutron in F19 with only a small disturbance of the core nucleons. The peaks at 14.0 and 19.1 Mev are interpreted as the components of a split giant resonance, indicating an intrinsic quadrupole moment, Q0, of approximately 0.30 × 10−21 cm2 for F19.