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. We find that while the host is a relatively luminous (L approximately 0.8 L* sub(B)), star-forming (SFR = 1.84 M sub(middot in circle) yr super(-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 (SFR; 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 neutron-star-neutron-star binary ("kilonova").