The Large Synoptic Survey Telescope (LSST) project is a proposed large-aperture, wide-field, ground-based telescope that will survey half the sky every few nights in six optical bands. LSST will produce a data set suitable for answering a wide range of pressing questions in astrophysics, cosmology, and fundamental physics. The 8.4-meter telescope will be located in the Andes mountains near La Serena, Chile. The 3.2 Gpixel camera will take 6.4 GB images every 15 seconds, resulting in 15 TB of new raw image data per night. An estimated 2 million transient alerts per night will be generated within 60 seconds of when the camera's shutter closes. Processing such a large volume of data, converting the raw images into a faithful representation of the universe, automated data quality assessment, automated discovery of moving or transient sources, and archiving the results in useful form for a broad community of users is a major challenge. We present an overview of the planned computing infrastructure for LSST. The cyberinfrastructure required to support the movement, storing, processing, and serving of hundreds of petabytes of image and database data is described. We also review the sizing model that was developed to estimate the hardware requirements to support this environment beginning during project construction and continuing throughout the 10 years of operations.