We present early optical photometry and spectroscopy of the afterglow and host galaxy of the bright short-duration gamma-ray burst GRB 130603B discovered by the Swift satellite . Using our Target of Opportunity program on the Gemini South telescope , our prompt optical spectra reveal a strong trace from the afterglow superimposed on continuum and emission lines from the z = 0.3568 \pm 0.0005 host galaxy . The combination of a relatively bright optical afterglow ( r ^ { \prime } = 21.52 at \Delta t = 8.4 hr ) , together with an observed offset of 0 \farcs 9 from the host nucleus ( 4.8 kpc projected distance at z = 0.3568 ) , allow us to extract a relatively clean spectrum dominated by afterglow light . Furthermore , the spatially resolved spectrum allows us to constrain the properties of the explosion site directly , and compare these with the host galaxy nucleus , as well as other short-duration GRB host galaxies . We find that while the host is a relatively luminous ( L \approx 0.8 L ^ { * } _ { B } ) , star-forming ( SFR = 1.84 { M } _ { \odot } { yr } ^ { -1 } ) galaxy with almost solar metallicity , the spectrum of the afterglow exhibits weak Ca ii absorption features but negligible emission features . The explosion site therefore lacks evidence of recent star formation , consistent with the relatively long delay time distribution expected in a compact binary merger scenario . The star formation rate ( both in an absolute sense and normalized to the luminosity ) and metallicity of the host are both consistent with the known sample of short-duration GRB hosts and with recent results which suggest GRB 130603B emission to be the product of the decay of radioactive species produced during the merging process of a NS-NS binary ( “ kilonova ” ) . Ultimately , the discovery of more events similar to GRB 130603B and their rapid follow-up from 8-m class telescopes will open new opportunities for our understanding of the final stages of compact-objects binary systems and provide crucial information ( redshift , metallicity and chemical content of their explosion site ) to characterize the environment of one of the most promising gravitational wave sources .