An unexpected feature common to 2H transition metal dichalcogenides (2H TMDs) is revealed with a first-principles Wannier function analysis of the electronic structure of the prototype 2H TaSe2: The low-energy Ta “5dz2” bands governing the physics of a charge-density wave (CDW) is dominated by hopping between next-nearest neighbors. With this motivation we develop a minimal effective model for the CDW formation, in which the unusual form of the hopping leads to an approximate decoupling of the three sublattices. In the CDW phase one sublattice remains undistorted, leaving the bands associated with it ungapped everywhere in the Fermi surface, resolving the long-standing puzzle of the coexistence of gapless excitations and commensurate CDW in the 2H TMDs.