The capability to isolate one to few unit-cell thin layers from the bulk matrix of layered compounds 1 opens fascinating prospects to engineer novel electronic phases. However, a comprehensive study of the thickness dependence and of potential extrinsic effects are paramount to harness the electronic properties of such atomic foils. One striking example is the charge density wave (CDW) transition temperature in layered dichalcogenides whose thickness dependence remains unclear in the ultrathin limit 2-5 .Here we present a detailed study of the thickness and temperature dependences of the CDW in VSe 2 by scanning tunnelling microscopy (STM). We show that mapping the real-space CDW periodicity over a broad thickness range unique to STM provides essential insight 6 . We introduce a robust derivation of the local order parameter and transition temperature based on the real space charge modulation amplitude. Both quantities exhibit a striking non-monotonic thickness dependence that we explain in terms of a 3D to 2D dimensional crossover in the FS topology. This finding highlights thickness as a true tuning parameter of the electronic ground state and reconciles seemingly contradicting thickness dependencies determined in independent transport studies.Following the ground-breaking exfoliation of graphite into one atom thin carbon sheets, an increasing number of layered compounds can now be isolated from their bulk matrix in the form of one to few unit-cell thin layers. These sheets often feature unique 7-9 or enhanced 2,10 properties in comparison to their parent bulk compounds. They depend on material thickness and can be further tuned through doping, electrostatic gating and assembly of distinct layers into complex heterostructures. Transition metal dichalcogenides (TMDs) are of particular interest in this context. They can be readily exfoliated into thin flakes down to the single unitcell limit 11 and offer a unique playground for studying the thickness dependence of their electronic properties. For example, in MoS 2 , photo active transitions become available in the