We report our analysis of MACS J0717.5+3745 using 140 and 268 GHz Bolocam data collected at the Caltech Submillimeter Observatory. We detect extended Sunyaev-Zeldovich (SZ) effect signal at high significance in both Bolocam bands, and we employ Herschel-SPIRE observations to subtract the signal from dusty background galaxies in the 268 GHz data. We constrain the two-band SZ surface brightness toward two of the sub-clusters of MACS J0717.5+3745: the main sub-cluster (named C), and a sub-cluster identified in spectroscopic optical data to have a line-of-sight velocity of +3200 km/s (named B). We determine the surface brightness in two separate ways: via fits of parametric models and via direct integration of the images. For both sub-clusters, we find consistent surface brightnesses from both analysis methods. We constrain spectral templates consisting of relativistically corrected thermal and kinetic SZ signals, using a jointly-derived electron temperature from Chandra and XMM-Newton under the assumption that each sub-cluster is isothermal. The data show no evidence for a kinetic SZ signal toward sub-cluster C, but they do indicate a significant kinetic SZ signal toward sub-cluster B. The model-derived surface brightnesses for sub-cluster B yield a best-fit line-of-sight velocity of v_z = +3450 +- 900 km/s, with (1 - Prob[v_z > 0]) = 1.3 x 10^-5 (4.2 sigma away from 0 for a Gaussian distribution). The directly integrated sub-cluster B SZ surface brightnesses provide a best-fit v_z = +2550 +- 1050 km/s, with (1 - Prob[v_z > 0]) = 2.2 x 10^-3 (2.9 sigma).
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