We report the first observation of the radiative charm decay D-0 -> rho(0)gamma and the first search for CP violation in decays D-0 -> rho(0)gamma, phi gamma, and (K) over bar (*0)(892)gamma, using a data sample of 943 fb(-1) collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The branching fraction is measured to be B(D-0 -> rho(0)gamma) = (1.77 +/- 0.30 +/- 0.07) x 10(-5), where the first uncertainty is statistical and the second is systematic. The obtained CP asymmetries A(CP)(D-0 ->rho(0)gamma) = +0.056 +/- 0.152 +/- 0.006, A(CP)(D-0 -> phi gamma) = -0.094 +/- 0.066 +/- 0.001, and A(CP)(D-0 -> (K) over bar (*0) gamma = -0.003 +/- 0.020 +/- 0.000 are consistent with no CP violation. We also present an improved measurement of the branching fractions B(D-0 -> phi gamma) = (2.76 +/- 0.19 +/- 0.10) x 10(-5) and B(D-0 -> (K) over bar (*0) gamma = (4.66 +/- 0.21 +/- 0.21) x 10(-4).