Originated as a philosophical quest, personality discerns how individuals differ from each other in terms of thinking, feeling, and behaving. Towards building social machines that work with humans on a daily basis, we are motivated to ask: (1) Do existing pre-trained language models possess personality, akin to their human counterpart? If so, (2) how can we evaluate them? Further, given this evaluation framework, (3) how can we induce a certain personality in a fully controllable fashion? To tackle these three questions, we propose the Machine Personality Inventory (MPI) dataset for evaluating the machine personality; MPI follows standardized personality tests, built upon the Big Five Personality Factors (Big Five) theory and personality assessment inventories. By evaluating models with MPI, we provide the first piece of evidence showing the existence of personality in pre-trained language models. We further devise a CHAIN PROMPTING method to induce the language model with a specific personality in a controllable manner, capable of producing diversified behaviors. We hope to shed light on future studies by adopting personality as the essential psychological guidance for various downstream tasks, building more human-like and in situ dialogue agents.