A convex polygon is a polygon whose vertices are points on the integer lattice with interior angles all convex. Let $a(v)$ be the least possible area of a convex lattice polygon with $v$ vertices. It is known that $cv^{2.5}\leq a(v)\leq (15/784)v^3 + o(v^3)$. In this paper, we prove that $a(v)\geq (1/1152)v^3 + O(v^2)$.