We present a density functional theory for mixtures of (hard sphere) colloidal particles and ideal polymers. For this extreme nonadditive system we employ a fundamental measures approach to construct a functional which incorporates the correct dimensional crossover and the exact low density limit. In bulk fluid mixtures the functional yields the same free energy and, therefore, the same gas-liquid (demixing) transition as given by free-volume theory. It generates consistent pair correlation functions; the partial structure factors Sij(k) diverge, as k→0, at the critical point obtained from the free energy. Our results for the structure agree well with those from simulation and Percus-Yevick theory.