For frequency selective interference channels where interference is treated as noise, distributively attaining the boundary of the rate region is an open problem, and is particularly important for broadband DSL access. This paper develops, analyzes, and simulates a new algorithm for power allocation in frequency selective interference channels called Autonomous Spectrum Balancing (ASB). It utilizes the concept of a "reference line", which mimics a typical victim line in the interference channel. Compared with the state-of-the-art Iterative Watefilling and Optimum Spectrum Balancing methods, the ASB algorithm is completely autonomous, has linear complexity in both the number of users and tones, and gives close to near-optimal performance. Convergence of a version of ASB is proven for any number of users.