We present a novel framework for recognizing personality traits based on users' physiological responses to affective movie clips. Extending studies that have correlated explicit/implicit affective user responses with Extraversion and Neuroticism traits, we perform single-trial recognition of the big-five traits from Electrocardiogram (ECG), Galvanic Skin Response (GSR), Electroencephalogram (EEG) and facial emotional responses compiled from 36 users using off-the-shelf sensors. Firstly, we examine relationships among personality scales and (explicit) affective user ratings acquired in the context of prior observations. Secondly, we isolate physiological correlates of personality traits. Finally, unimodal and multimodal personality recognition results are presented. Personality differences are better revealed while analyzing responses to emotionally homogeneous (e.g., high valence, high arousal) clips, and significantly above-chance recognition is achieved for all five traits.