Question answering over knowledge graph (KGQA) aims at answering natural language questions posed over knowledge graphs (KGs). Moreover, multi-hop KGQA requires reasoning across multiple triplets in KGs to get to the answer. Unfortunately, KGs often lack complete information and contain many missing links, which poses huge challenges for multi-hop KGQA. To address this, recent several approaches have introduced KG embedding techniques, which have shown good performance on the multi-hop KGQA task. However, these methods ignore the semantic correlations between paths and questions, and the reasoning process is not easily explained. Furthermore, traditional KG embedding methods consider only low-order pairwise relations and ignore the higher-order relations among entities, leading to a sub-optimal embedding result. To address these problems, we propose Hic-KGQA, a novel hypergraph and inference chain-based model for multi-hop KGQA. Specifically, Hic-KGQA first generates pre-trained entity embeddings with multiple semantics via a hypergraph-based KGC module (HKM). Then, an inference chain modeling module (ICMM) is designed to learn the importance of different inference chains for the question and encode the highest-ranked inference chain into an embedding representation. Finally, two scoring networks are used to evaluate the correlation between the candidate answers and the questions from the perspective of both the triplet facts and the reasoning process to obtain more accurate answers. Furthermore, the mutual information maximization (MIM) is innovatively implemented to capture richer common path features from similar cases to alleviate the missing path problem caused by KG incompleteness. Experiments show that Hic-KGQA significantly outperforms existing state-of-the-art methods and is explainable.