The adoption of differential privacy is growing but the complexity of designing private, efficient and accurate algorithms is still high. We propose a novel programming framework and system, εktelo, for implementing both existing and new privacy algorithms. For the task of answering linear counting queries, we show that nearly all existing algorithms can be composed from operators, each conforming to one of a small number of operator classes. While past programming frameworks have helped to ensure the privacy of programs, the novelty of our framework is its significant support for authoring accurate and efficient (as well as private) programs. After describing the design and architecture of the εktelo system, we show that εktelo is expressive, allows for safer implementations through code reuse, and that it allows both privacy novices and experts to easily design algorithms. We demonstrate the use of εktelo by designing several new state-of-the-art algorithms.