Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe_{2}, which shows a (sqrt[7]×sqrt[3]) CDW in contrast to the (4×4) CDW for the layers in bulk VSe_{2}. Angle-resolved photoemission spectroscopy from the single layer shows a sizable (sqrt[7]×sqrt[3]) CDW gap of ∼100  meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.