We propose to build a compact, high-precision single-axis accelerometer based on atom interferometry that is applicable to operation in space environments. Based on our successful Phase I design, the proposed accelerometer emphasizes reliable operation and exceptional acceleration sensitivity. It incorporates several innovative features that make it appropriate for a variety of space-based and terrestrial applications. Phase II will result in a completed sensor build, including a sensor head, laser system and electronic control system. Space-based inertial sensors based on atom interferometry are a compelling technology for both technological and scientific applications because of the exceptionally high performance that can be enabled by long interrogation times with cold atoms in a microgravity environment.