We introduce Zurich Atmosphere Purge (ZAP), an approach to sky subtraction based on principal component analysis (PCA) that we have developed for the Multi Unit Spectrographic Explorer (MUSE) integral field spectrograph. ZAP employs filtering and data segmentation to enhance the inherent capabilities of PCA for sky subtraction. Extensive testing shows that ZAP reduces sky emission residuals while robustly preserving the flux and line shapes of astronomical sources. The method works in a variety of observational situations from sparse fields with a low density of sources to filled fields in which the target source fills the field of view. With the inclusion of both of these situations, the method is generally applicable to many different science cases and should also be useful for other instrumentation. ZAP is available for download at http://muse-vlt.eu/science/tools.