The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields H applied perpendicular to the ab plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy performed on the same crystal demonstrates that the order parameter vanishes at the surface upon entering the high-field phase. These results provide the first demonstration of a pinned planar node perpendicular to H, which is consistent with a putative FFLO state.