This problem appears in Croot and Lev's 2007 "Open Problems in Additive Combinatorics" (http://people.math.gatech.edu/~ecroot/E2S-01-11.pdf ), where it is attributed to Erdos and Graham (the latter of whom offers $250 for its solution).
Other references may include Cooper and Poirel's "Notes on the Pythagorean Triple System" (http://www.math.sc.edu/~cooper/pth.pdf ), which mentions that even the case of whether 2 colors is enough is open. They also exhibit a 2-coloring of the integers from 1 to 1344 without any monochromatic Pythagorean triples.