Heterogeneous information network (HIN) embedding, aiming to project HIN into a low-dimensional space, has attracted considerable research attention. Most of the exiting HIN embedding methods focus on preserving the inherent network structure and semantic correlations in Euclidean spaces. However, one fundamental problem is that whether the Euclidean spaces are the appropriate or intrinsic isometric spaces of HIN? Recent researches argue that the complex network may have the hyperbolic geometry underneath, because the underlying hyperbolic geometry can naturally reflect some properties of complex network, e.g., hierarchical and power-law structure. In this paper, we make the first effort toward HIN embedding in hyperbolic spaces. We analyze the structures of two real-world HINs and discover some properties, e.g., the power-law distribution, also exist in HIN. Therefore, we propose a novel hyperbolic heterogeneous information network embedding model. Specifically, to capture the structure and semantic relations between nodes, we employ the meta-path guided random walk to sample the sequences for each node. Then we exploit the distance in hyperbolic spaces as the proximity measurement. The hyperbolic distance is able to meet the triangle inequality and well preserve the transitivity in HIN. Our model enables the nodes and their neighborhoods have small hyperbolic distances. We further derive the effective optimization strategy to update the hyperbolic embeddings iteratively. The experimental results, in comparison with the state-of-the-art, demonstrate that our proposed model not only has superior performance on network reconstruction and link prediction tasks but also shows its ability of capture hierarchy structure in HIN via visualization.