Spitzer observations of the neutron star (ultracompact) X-ray binary (XRB) 4U 0614+091 with the Infrared Array Camera reveal emission of nonthermal origin in the range 3.5-8 μm. The mid-infrared spectrum is well fit by a power law with spectral index of α=-0.57+/-0.04 (where the flux density is Fν~να). Given the ultracompact nature of the binary system, we exclude the possibility that either the companion star or the accretion disk can be the origin of the observed emission. These observations represent the first spectral evidence for a compact jet in a low-luminosity neutron star XRB and furthermore of the presence, already observed in two black hole (BH) XRBs, of a ``break'' in the synchrotron spectrum of such compact jets. We can derive a firm upper limit on the break frequency of the spectrum of νthin=3.7×1013 Hz, which is lower than that observed in BH XRBs by at least a factor of 10. Assuming a high-energy cooling cutoff at ~1 keV, we estimate a total (integrated up to X-rays) jet power to X-ray bolometric luminosity ratio of ~5%, much lower than that inferred in BHs.