The heat conductance of a ballistic one-dimensional channel is a quantity that depends only on universal constants,κ = π²k_B²T/3h. It was predicted not to depend on the exchange statistics of the heat-carrying particles or on the strength of their mutual interaction. This had been verified experimentally only for weakly interacting systems of phonons, photons and electronic Fermi-liquids. We report here the first observation of quantized heat flow in a strongly interacting system of 2D electrons in the fractional quantum Hall effect regime. We observed such quantization of the chiral edge modes in a particle-like Laughlin state (filling 1/3) and in several hole-like states with fillings between ½ and 1; with the latter harbor counter-propagating neutral (chargeless) modes. The observed heat conductance of both, fractionally charged and neutral modes, is quantized as expected. Moreover, the measure total thermal conductance of each state was found to agree with the predicted value.