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We present radio, optical/NIR, and X-ray observations of the afterglow of the short-duration 130603B, and uncover a break in the radio and optical bands at 0.5 d after the burst, best explained as a jet break with an inferred jet opening angle of 4-8 deg. GRB 130603B is only the third short GRB with a radio afterglow detection to date, and the first time that a jet break is evident in the radio band. We model the temporal evolution of the spectral energy distribution to determine the burst explosion properties and find an isotropic-equivalent kinetic energy of (0.6-1.7) x 10^51 erg and a circumburst density of 5 x 10^-3-30 cm^-3. From the inferred opening angle of GRB 130603B, we calculate beaming-corrected energies of Egamma (0.5-2) x 10^49 erg and EK (0.1-1.6) x 10^49 erg. Along with previous measurements and lower limits we find a median short GRB opening angle of 10 deg. Using the all-sky observed rate of 10 Gpc^-3 yr^-1, this implies a true short GRB rate of 20 yr^-1 within 200 Mpc, the Advanced LIGO/VIRGO sensitivity range for neutron star binary mergers. Finally, we uncover evidence for significant excess emission in the X-ray afterglow of GRB 130603B at >1 d and conclude that the additional energy component could be due to fall-back accretion or spin-down energy from a magnetar formed following the merger., Submitted to ApJ; emulateapj style; 10 pages, 1 table, 3 figures