Left-right laterality is an important aspect of human –and in fact all vertebrate– brain organization for which the genetic basis is poorly understood. Using RNA sequencing data we contrasted gene expression in left- and right-sided samples from several structures of the anterior central nervous systems of post mortem human embryos and foetuses. While few individual genes stood out as significantly lateralized, most structures showed evidence of laterality of their overall transcriptomic profiles. These left-right differences showed overlap with age-dependent changes in expression, indicating lateralized maturation rates, but not consistently in left-right orientation over all structures. Brain asymmetry may therefore originate in multiple locations, or if there is a single origin, it is earlier than 5 weeks post conception, with structure-specific lateralized processes already underway by this age. This pattern is broadly consistent with the weak correlations reported between various aspects of adult brain laterality, such as language dominance and handedness.