We report neutron scattering measurements on single crystals of BaFe1.92Co0.08As2. The magnetic Bragg peak intensity is reduced by 6% upon cooling through TC. The spin dynamics exhibit a gap of 8 meV with anisotropic three-dimensional interactions. Below TC additional intensity appears at an energy of approximately 4.5(0.5) meV, similar to previous observations of a spin resonance in other Fe-based superconductors. No further gapping of the spin excitations is observed below TC for energies down to 2 meV. These observations suggest the redistribution of spectral weight from the magnetic Bragg position to a spin resonance, demonstrating the direct competition between static magnetic order and superconductivity.