The Cooper pairing mechanism of heavy-fermion superconductors, while long hypothesized as due to spin fluctuations, has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap delta(k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure delta(k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging, a proven technique for measuring the energy gaps of high-Tc superconductors, has recently been proposed as a new method to measure delta(k) in heavy-fermion superconductors, specifically CeCoIn5. By implementing this method, we immediately detect a superconducting energy gap whose nodes are oriented along k||(+-1, +-1)pi/a0 directions. Moreover, we determine the complete k-space structure of the delta(k) of a heavy-fermion superconductor. For CeCoIn5, this novel information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that highest magnitude delta(k) opens on a high-k band so that gap nodes occur at quite unanticipated k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with dx2-y2 gap symmetry. The availability of such quantitative heavy band- and gap-structure data will be critical in identifying the microscopic mechanism of heavy fermion superconductivity in this material, and perhaps in general.