  Recently superconductivity and topological charge-density wave (CDW) were
discovered in the Kagome metals $A$V$_3$Sb$_5$ ($A$ = Cs, Rb, and K), which
have an ideal Kagome lattice of vanadium. Here we report resistance
measurements on thin flakes of CsV$_3$Sb$_5$ to investigate the evolution of
superconductivity and CDW with sample thickness. The CDW transition temperature
${\it T}_{\rm CDW}$ decreases from 94 K in bulk to a minimum of 82 K at
thickness of 60 nm, then increases to 120 K as the thickness is reduced further
to 4.8 nm (about five monolayers). Since the CDW order in CsV$_3$Sb$_5$ is
quite three-dimensional (3D) in the bulk sample, the non-monotonic evolution of
${\it T}_{\rm CDW}$ with reducing sample thickness can be explained by a 3D to
2D crossover around 60 nm. Strikingly, the superconducting transition
temperature ${\it T}_{\rm c}$ shows an exactly opposite evolution, increasing
from 3.64 K in the bulk to a maximum of 4.28 K at thickness of 60 nm, then
decreasing to 0.76 K at 4.8 nm. Such exactly opposite evolutions provide strong
evidence for competing superconductivity and CDW, which helps us to understand
these exotic phases in $A$V$_3$Sb$_5$ Kagome metals.
