We report SMARTS, Gemini, and Swift-UVOT observations of the optical transient (OT) associated with gamma-ray burst (GRB) 091127, at redshift 0.49, taken between 0.9 hr and 102 days following the Swift trigger. In our early-time observations, the OT fades in a manner consistent with previously observed GRB afterglows. However, after nine days post-burst, the OT is observed to brighten for a period of åisebox-0.5ex two weeks, after which the source resumes fading. A comparison of this late-time ``bump’’ to SN 1998bw (the broad-lined Type Ic supernova associated with GRB 980425), and several other GRB supernovae (SNe), indicates that the most straightforward explanation is that GRB 091127 was accompanied by a contemporaneous SN (SN 2009nz) that peaked at a magnitude of M$_V$ = -19.0 ± 0.2. SN 2009nz is globally similar to other GRB SNe, but evolves slightly faster than SN 1998bw and reaches a slightly dimmer peak magnitude. We also analyze the early-time UV-optical-IR spectral energy distribution of the afterglow of GRB 091127 and find that there is little to no reddening in the host galaxy along the line of sight to this burst.