The cuprates and iron-based high-temperature superconductors share many common features: layered strongly anisotropic crystal structure, strong electronic correlations, interplay between different types of electronic ordering, the intrinsic spatial inhomogeneity due to doping. The understanding of complex interplay between these factors is crucial for a directed search of new high-temperature superconductors. Here we show the appearance of inhomogeneous gossamer superconductivity in bulk FeSe compound at ambient pressure and at temperature 5 times higher than its zero-resistance $T_c$. This discovery helps to understand numerous remarkable superconducting properties of FeSe. We also find and prove a general property: if inhomogeneous superconductivity in a anisotropic conductor first appears in the form of isolated superconducting islands, it reduces electric resistivity anisotropically with maximal effect along the least conducting axis. This gives a simple and very general tool to detect inhomogeneous superconductivity in anisotropic compounds, which is critically important to study the onset of high-temperature superconductivity.