We experimentally and theoretically determine the magic wavelength of the (5s(2))S-1(0) - (5s5p)P-3(0) clock transition of Cd-111 to be 419.88(14) and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the S-1(0) - P-3(1) transition to cool the atoms to 6 mu K and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate the blackbody shift, including the dynamic correction, to be fractionally 2.83(8) x 10(-16) at 300 K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd P-1(1) lifetime and the ground state C-6 coefficient.