We report the measurement of the Cabibbo-Kobayashi-Maskawa CP-violating angle γ through a Dalitz plot analysis of neutral D-meson decays to K(S)(0) π+ π- and K(S)(0) K+ K- produced in the processes B∓ → DK∓, B∓ D* K∓ with D* → Dπ(0), Dγ, and B∓ → DK*∓ with K*∓ → K(S)(0) π∓, using 468 million BB pairs collected by the BABAR detector at the PEP-II asymmetric-energy e+ e- collider at SLAC. We measure γ = (68 ± 14 ± 4 ± 3)° (modulo 180°), where the first error is statistical, the second is the experimental systematic uncertainty, and the third reflects the uncertainty in the description of the neutral D decay amplitudes. This result is inconsistent with γ = 0 (no direct CP violation) with a significance of 3.5 standard deviations.