BG-MO 2013 Problem 3

The integer lattice in the plane is colored with 3 colors. Find the least positive real $S$ with the property: for any such coloring it is possible to find a monochromatic lattice points $A,B,C$ with $S_{\triangle ABC}=S$ .

Proposed by Nikolay Beluhov

EDIT: It was the problem 3 (not 2), corrected the source title.