Research on trust between humans and machines has primarily investigated factors relating to environmental or system characteristics, largely neglecting individual differences that play an important role in human behavior and cognition. This study examines the role of the Big Five personality traits on trust in a partnership between a human user and a humanoid robot. A Wizard of Oz methodology was used in an experiment to simulate an artificially intelligent robot that could be leveraged as a partner to complete a life or death survival simulation. Eye-tracking was employed to measure system utilization and validated psychometric instruments were used to measure trust and personality traits. Results suggest that individuals scoring high on the openness personality trait may have greater trust in a humanoid robot partner than those with low scores in the openness personality dimension.