We present NMR data in the normal and superconducting states of CeCoIn5 for fields close to Hc2(0)=11.8T in the ab plane. Recent experiments identified a first-order transition from the normal to superconducting state for H>10.5T, and a new thermodynamic phase below 290 mK within the superconducting state. We find that the Knight shifts of the In(1), In(2), and the Co are discontinuous across the first-order transition and the magnetic linewidths increase dramatically. The broadening differs for the three sites, unlike the expectation for an Abrikosov vortex lattice, and suggests the presence of static spin moments in the vortex cores. In the low-temperature and high-field phase, the broad NMR lineshapes suggest ordered local moments, rather than a long-wavelength quasiparticle spin density modulation expected for an FFLO phase.