Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here, we use the muon spin rotation/relaxation (μSR) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier μSR studies on powders and crystals, we show that while the superconducting gap is most probably anisotropic but nodeless along the crystallographic c axis, it is nodal in the ab plane, as indicated by the linear increase of the superfluid density at low temperature. We further show that the superconducting properties of FeSe display a less pronounced anisotropy than expected.