Human players in professional team sports achieve high level coordination by dynamically choosing complementary skills and executing primitive actions to perform these skills. As a step toward creating intelligent agents with this capability for fully cooperative multi-agent settings, we propose a two-level hierarchical multi-agent reinforcement learning (MARL) algorithm with unsupervised skill discovery. Agents learn useful and distinct skills at the low level via independent Q-learning, while they learn to select complementary latent skill variables at the high level via centralized multi-agent training with an extrinsic team reward. The set of low-level skills emerges from an intrinsic reward that solely promotes the decodability of latent skill variables from the trajectory of a low-level skill, without the need for hand-crafted rewards for each skill. For scalable decentralized execution, each agent independently chooses latent skill variables and primitive actions based on local observations. Our overall method enables the use of general cooperative MARL algorithms for training high level policies and single-agent RL for training low level skills. Experiments on a stochastic high dimensional team game show the emergence of useful skills and cooperative team play. The interpretability of the learned skills show the promise of the proposed method for achieving human-AI cooperation in team sports games.