We report on a study of exclusive radiative decays of the Y(1S) resonance c
ollected with the CLEO II detector operating at the Cornell Electron Storag
e Ring. We present the first observation of the radiative decays Y(1S) -->
gamma pi(+)pi(-) and Y(1S) --> gamma pi(0)pi(0). For the dipion mass regime
m(pi pi) > 1.0 GeV, we obtain N(Y(1S) --> gamma pi(+)pi(-)) = (6.3 +/- 1.2
+/- 1.3) x 10(-5) and B(Y(1S) --> gamma pi(0)pi(0)) = (1.7 +/- 0.6 +/- 0.3
) x 10(-5).