The electron-ion recombination rate coefficient for Si IV forming Si III was measured at the heavy-ion storage-ring TSR. The experimental electron-ion collision energy range of 0-186 eV encompassed the 2p(6) nl nl dielectronic recombination (DR) resonances associated with 3s to nl core excitations, 2s 2p(6) 3s nl nl resonances associated with 2s to nl (n=3,4) core excitations, and 2p(5) 3s nl nl resonances associated with 2p to nl (n=3,...,infinity) core excitations. The experimental DR results are compared with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) method for DR via the 3s to 3p nl and 3s to 3d nl (both n=3,...,6) and 2p(5) 3s 3l nl (n=3,4) capture channels. Finally, the experimental and theoretical plasma DR rate coefficients for Si IV forming Si III are derived and compared with previously available results.