In two-dimensional van der Waals (vdW) magnets, the presence of magnetic orders, strong spin-orbit coupling and asymmetry at interfaces is the key ingredient for hosting chiral spin textures. However, experimental evidences for chiral magnetism in vdW magnets remain elusive. Here we demonstrate unambiguously the formation of chiral spin textures in thin Fe3GeTe2 nanoflakes using advanced magnetic electron microscopy and first-principles calculations. Specifically, electron holography analyses reveal the spin configurations of Neel-type, zero-field-stabilized skyrmions in 20-nm-thick Fe3GeTe2 nanoflakes at cryogenic temperature. In situ Lorentz transmission electron microscopy measurements further provide detailed magnetic phase diagrams of chiral spin textures including spirals and skyrmions in Fe3GeTe2 as a function of temperature, applied magnetic field and specimen thickness. First-principles calculations unveil a finite interfacial Dzyaloshinskii-Moriya interaction in the Te/Fe3Ge/Te slabs that induces the spin chirality in Fe3GeTe2. Our discovery of spin chirality in the prototypical vdW Fe3GeTe2 opens up new opportunities for studying chiral magnetism in two-dimensional vdW magnets from both fundamental and applied perspectives.