Past research has demonstrated that human subjects tend to be poor at generating random sequences, though there are marked individual differences. One variable which may partially account for these individual differences is hemispheric preference. The description of the cognitive state that facilitates ability to generate random sequences resembles in a number of respects the mode of cognitive processing of the right hemisphere. On this premise, the present investigation hypothesized that left lookers on the Conjugate Lateral Eye Movement test, those showing a right hemisphere preference, would generate more random sequences. The subjects were 40 male and 40 female right handed university students. As predicted, left looking was significantly correlated with more random sequence generation. It was suggested that left lookers may utilize a more diffuse mode of attention and may be less likely to apply erroneous subjective concepts of randomness on the sequence generation task.