Motivation: Copy number alterations (CNAs) are a significant driver in cancer growth and development, but remain poorly characterized on the single cell level. Although genome evolution in cancer cells is Markovian through evolutionary time, CNAs are not Markovian along the genome. However, existing methods call copy number profiles with Hidden Markov Models or change point detection algorithms based on changes in observed read depth, corrected by genome content and do not account for the stochastic evolutionary process. Results: We present a theoretical framework to use tumor evolutionary history to accurately call CNAs in a principled manner. To model the tumor evolutionary process and account for technical noise from low coverage single-cell whole genome sequencing data, we developed SCONCE, a method based on a Hidden Markov Model to analyze read depth data from tumor cells using matched normal cells as negative controls. Using a combination of public data sets and simulations, we show SCONCE accurately decodes copy number profiles, and provides a useful tool for understanding tumor evolution. Availabilityand implementation: SCONCE is implemented in C++11 and is freely available from https://github.com/NielsenBerkeleyLab/sconce.