  We report experimental evidence of charge density wave (CDW) transition in
monolayer 1T-VTe$_2$ film. 4$\times$4 reconstruction peaks are observed by low
energy electron diffraction below the transition temperature $T_{CDW}$ = 186 K.
Angle-resolved photoemission spectroscopy measurements reveal arc-like pockets
with anisotropic CDW gaps up to 50 meV. The anisotropic CDW gap is attributed
to the imperfect nesting of the CDW wave vector, and first-principles
calculations reveal phonon softening at the same vector, suggesting the
important roles of Fermi surface nesting and electron-phonon interaction in the
CDW mechanism.
