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With increased globalization and labor mobility, human resource reallocation across firms, industries and regions has become the new norm in labor markets. The emergence of massive digital traces of such mobility offers a unique opportunity to understand labor mobility at an unprecedented scale and granularity. While most studies on labor mobility have largely focused on characterizing macro-level (e.g., region or company) or micro-level (e.g., employee) patterns, the problem of how to accurately predict an employee's next career move (which company with what job title) receives little attention. This paper presents the first study of large-scale experiments for predicting next career moves. We focus on two sources of predictive signals: profile context matching and career path mining and propose a contextual LSTM model, NEMO, to simultaneously capture signals from both sources by jointly learning latent representations for different types of entities (e.g., employees, skills, companies) that appear in different sources. In particular, NEMO generates the contextual representation by aggregating all the profile information and explores the dependencies in the career paths through the Long Short-Term Memory (LSTM) networks. Extensive experiments on a large, real-world LinkedIn dataset show that NEMO significantly outperforms strong baselines and also reveal interesting insights in micro-level labor mobility.