The Sunyaev–Zel'dovich (SZ) effect spectrum crosses through a null where ΔT CMB= 0 near ν 0= 217 GHz. In a cluster of galaxies, ν 0 can be shifted from the canonical thermal SZ effect value by corrections to the SZ effect scattering due to the properties of the inter-cluster medium. We have measured the SZ effect in the hot galaxy cluster RX J 1347.5− 1145 with Z-Spec, an R∼ 300 grating spectrometer sensitive between 185 and 305 GHz. These data comprise a high spectral resolution measurement around the null of the SZ effect and clearly exhibit the transition from negative to positive ΔT CMB over the Z-Spec band. The SZ null position is measured to be ν 0= 225.8±2.5 (stat.)±1.2 (sys.) GHz, which differs from the canonical null frequency by 3.0 σ and is evidence for modifications to the canonical thermal SZ effect shape. Assuming the measured shift in ν 0 is due only to relativistic corrections to the SZ spectrum, we place the limit kT e= 17.1±5.3 keV from the zero-point measurement alone. By simulating the response of the instrument to the sky, we are able to generate likelihood functions in {y 0, T e, v pec} space. For v pec= 0 km s− 1, we measure the best-fitting SZ model to be y 0= 4.6+ 0.6− 0.9× 10− 4, T e, 0= 15.2+ 12− 7.4 keV. When v pec is allowed to vary, a most probable value of v pec=+ 450±810 km s− 1 is found.