Predictions of a topological electronic structure in the skutterudite TPn3 family (T=transition metal, Pn=pnictogen) are investigated via magnetoresistance, quantum oscillation, and angle-resolved photoemission experiments on RhSb3, a semimetal with low carrier density. Electronic band structure calculations and symmetry analysis of RhSb3 indicate this material to be a zero-gap semimetal protected by symmetry with inverted valence and conduction bands that touch at the Γ point close to the Fermi level. Transport experiments reveal an unsaturated linear magnetoresistance that approaches a factor of 200 at 60 T magnetic fields and quantum oscillations observable up to 150 K that are consistent with a large Fermi velocity (∼1.3×106 m/s), high carrier mobility [∼14 m2/(Vs)], and the existence of a small three-dimensional hole pocket. A very small, sample-dependent effective mass falls to values as low as 0.018(2) of the bare electron mass and scales with the Fermi wave vector. This, together with a nonzero Berry's phase and the location of the Fermi level in the linear region of the valence band, suggests RhSb3 as representative of a material family of topological semimetals with symmetry-enforced Fermi degeneracy at the high-symmetry points.