An interaction between electrons and lattice vibrations (phonons) results in two fundamental quantum phenomena in solids: in three dimensions it can turn a metal into a superconductor whereas in one dimension it can turn a metal into an insulator. In two dimensions (2D) both superconductivity and charge-density waves (CDW) are believed to be anomalous. In superconducting cuprates, critical transition temperatures are unusually high and the energy gap may stay unclosed even above these

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... es (pseudogap). In CDW-bearing dichalcogenides the resistivity below the transition can decrease with temperature even faster than in the normal phase and a basic prerequisite for the CDW, the favourable nesting conditions (when some sections of the Fermi surface appear shifted by the same vector), seems to be absent. Notwithstanding the existence of alternatives to conventional theories, both phenomena in 2D still remain the most fascinating puzzles in condensed matter physics. Using the latest developments in high-resolution angle-resolved photoemission spectroscopy (ARPES) here we show that the normal-state pseudogap also exists in one of the most studied 2D examples, dichalcogenide 2H-TaSe2, and the formation of CDW is driven by a conventional nesting instability, which is masked by the pseudogap. Our findings reconcile and explain a number of unusual, as previously believed, experimental responses as well as disprove many alternative theoretical approaches. The magnitude, character and anisotropy of the 2D-CDW pseudogap are intriguingly similar to those seen in superconducting cuprates.