Open relation extraction (OpenRE) aims to extract novel relation types from open-domain corpora, which plays an important role in completing the relation schemes of knowledge bases (KBs). Most OpenRE methods cast different relation types in isolation without considering their hierarchical dependency. We argue that OpenRE is inherently in close connection with relation hierarchies. To establish the bidirectional connections between OpenRE and relation hierarchy, we propose the task of open hierarchical relation extraction and present a novel OHRE framework for the task. We propose a dynamic hierarchical triplet objective and hierarchical curriculum training paradigm, to effectively integrate hierarchy information into relation representations for better novel relation extraction. We also present a top-down hierarchy expansion algorithm to add the extracted relations into existing hierarchies with reasonable interpretability. Comprehensive experiments show that OHRE outperforms state-of-the-art models by a large margin on both relation clustering and hierarchy expansion.