Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. Here we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe2. We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid.