Cold-start recommendation has been a challenging problem due to sparse user-item interactions for new users or items. Existing efforts have alleviated the cold-start issue to some extent, most of which approach the problem at the data level. Earlier methods often incorporate auxiliary data as user or item features, while more recent methods leverage heterogeneous information networks (HIN) to capture richer semantics via higher-order graph structures. On the other hand, recent meta-learning paradigm sheds light on addressing cold-start recommendation at the model level, given its ability to rapidly adapt to new tasks with scarce labeled data, or in the context of cold-start recommendation, new users and items with very few interactions. Thus, we are inspired to develop a novel meta-learning approach named MetaHIN to address cold-start recommendation on HINs, to exploit the power of meta-learning at the model level and HINs at the data level simultaneously. The solution is non-trivial, for how to capture HIN-based semantics in the meta-learning setting, and how to learn the general knowledge that can be easily adapted to multifaceted semantics, remain open questions. In MetaHIN, we propose a novel semantic-enhanced tasks constructor and a co-adaptation meta-learner to address the two questions. Extensive experiments demonstrate that MetaHIN significantly outperforms the state of the arts in various cold-start scenarios. (Code and dataset are available at https://github.com/rootlu/MetaHIN.)