We report measurements of the capture barrier for the DX center in Si-doped AlxGa1-xAs as a function of the alloy composition. A model of the capture process which requires a distribution of capture barrier heights has been fit to the data for samples with x=0.35. A simple technique is used to extract the average capture barrier height from data for samples with AlAs mole fraction ranging from x=0.27 to x=0.55. The barrier height varies strongly with the composition and has a minimum at x=0.35. The implications of these results are discussed.