This paper presents a novel open-domain dialogue generation model emphasizing the differentiation of speakers in multi-turn conversations. Differing from prior work that solely relies on the content of conversation history to generate a response, we argue that capturing relative social relations among utterances (i.e., generated by either the same speaker or different persons) benefits the machine capturing fine-grained context information from a conversation history to improve context coherence in the generated response. Given that, we propose a speaker-aware Parallel Hierarchical Attentive Encoder-Decoder (PHAED) model that aims to model each utterance with the awareness of its speaker and contextual associations with the same speaker's previous messages. Specifically, in a conversation involving two speakers, we regard the utterances from one speaker as responses and those from the other as queries. After understanding queries via our encoder with inner-query and inter-query encodings, our decoder reuses the hidden states of previously generated responses, instead of reconstructing these by the encoder, to generate a new response. Our empirical results show that PHAED outperforms the state-of-the-art in both automatic and human evaluations. Furthermore, our ablation study shows that dialogue models with speaker tokens can generally decrease the possibility of generating non-coherent responses regarding the conversation context.