In this paper, we present a power allocation method for a distributed antenna system (DAS) to maximize energy efficiency (EE) which is defined as the ratio of the transmission rate to the total consumed power. Different from conventional EE maximization schemes which require iterative numerical methods, we derive the optimal solution as closed form by solving Karush-Kuhn-Tucker conditions. The obtained closed form expression is applicable to DAS with an arbitrary number of distributed antenna (DA) ports and general per-DA port power constraints, and is also guaranteed to be globally optimum. Through Monte Carlo simulations, we show that the proposed power allocation method produces the optimal average EE identical to exhaustive search with significantly reduced computational complexity. In addition, we demonstrate that DAS is more beneficial in terms of EE compared to conventional antenna systems.