By stretching the point, this could apply to the 1856 election. However, it would be more accurate to say that there was one active party involved, the Democrats, and two half-parties, the Whigs in an advanced state of dissolution, and the Republicans just forming. There was never a time when the GOP filled the classic role of a 3rd-party against two established ones.
There was in the sense that many Republicans came out of the Free-Soil Party.