A test of the second postulate of special relativity, the universality of the speed of light, using the Experiment on Timing Ranging and Atmospheric Sounding payload to be flown on board a terrestrial satellite is proposed. The propagation time of a light signal transmitted from one point to another without reflection would be measured directly by comparing the phases of two hydrogen maser clocks, one on board and one on the ground, using a laser or microwave time transfer system. An estimated uncertainty budget of the proposed measurements is given, resulting in an expected sensitivity of the experiment of \ensuremath{\delta}c/c1.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$. The proposed test would require no equipment additional to what is already planned and so is of inherently low cost.