Inelastic neutron scattering measurements on single crystals of superconducting BaFe1.84Co0.16As2 reveal a magnetic excitation located at wave vectors (1/2 1/2 L) in tetragonal notation. On cooling below T_{C}, a clear resonance peak is observed at this wave vector with an energy of 8.6(0.5) meV, corresponding to 4.5(0.3) k_{B}T_{C}. This is in good agreement with the canonical value of 5 k_{B}T_{C} observed in the cuprates. The spectrum shows strong dispersion in the tetragonal plane but very weak dispersion along the c axis, indicating that the magnetic fluctuations are two dimensional in nature. This is in sharp contrast to the anisotropic three dimensional spin excitations seen in the undoped parent compounds.