Monochromatic Triangles

For any (planar) triangle $T$, is there is a $3$-coloring of the (infinite) plane with no monochromatic copy of $T$? We imagine congruent copies of $T$ moved around the plane via rigid motions, and seek a spot where $T$ is monochromatic. $T$ is monochromatic if its three vertices are painted the same color, by virtue of lying on points of the plane painted that color. Note that the coloring in the question may depend on the given triangle $T$.