Many vertebrates present behavioural asymmetries (i.e. functional and/or structural specializations of left and right sides of the brain); however, evidence for arthropods is scarce. Some behavioural asymmetries can be correlated with morphology. A better understanding of behavioural asymmetries would be a crucial step to understand the evolution of brain asymmetries. Here, we investigated behavioural asymmetries of adult males of a mygalomorph Brachypelma albopilosum. First, as the time budgets of these active hunting spiders had not yet been documented, we established the temporal distribution of males’ motor activity to be able to test them when they were active. Their motor activity peaks during the night and again early morning (around 3 h and 10 h local time). Then, choice tests in a T-maze assessed the effects of light and of odours separately. Our results revealed that male tarantulas’ activity increased when they perceived light or the odour of conspecific females. Latencies to enter into the T-maze were shorter when a light cue was present and even shorter when odour cues (of prey or of conspecifics) were present. Choice between two identical cues (light or female odours) in a T-maze revealed, for the first time, their right behavioural laterality. Surprisingly, no significant external morphological differences could be evidenced between left and right eyes, lengths of the first legs or densities of mechanoreceptors and chemoreceptors on the tarsi of males’ first legs to suggest perceptual asymmetry supporting this behavioural asymmetry. This is the first report concerning tarantulas’ behavioural laterality.