The heavy-electron superconductor CeCoIn5 exhibits a puzzling precursor state above its superconducting critical temperature at T c≤2.3 K. The thermopower and Nernst signal are anomalous. Below 15 K, the entropy current of the electrons undergoes a steep decrease reaching ∼0 at Tc. Concurrently, the off-diagonal thermoelectric current αxy is enhanced. The delicate sensitivity of the zero-entropy state to field implies phase coherence over large distances. The prominent anomalies in the thermoelectric current contrast with the relatively weak effects in the resistivity and magnetization.