We present a market-based approach to the Air Traffic Flow Management (ATFM) problem. The goods in our market are delays and buyers are airline companies; the latter pay money to the FAA to buy away the desired amount of delay on a per flight basis. We give a notion of equilibrium for this market and an LP whose solution gives an equilibrium allocation of flights to landing slots as well as equilibrium prices for the landing slots. Via a reduction to matching, we show that this equilibrium can be computed combinatorially in strongly polynomial time. Moreover, there is a special set of equilibrium prices, which can be computed easily, that is identical to the VCG solution, and therefore the market is incentive compatible in dominant strategy.