While the ability of naturally ranging animals to recall the location of food resources and use straight-line routes between them has been demonstrated in several studies [1, 2], it is not known whether animals can use knowledge of their landscape to walk least-cost routes [3]. This ability is likely to be particularly important for animals living in highly variable energy landscapes, where movement costs are exacerbated [4, 5].  Here, we used least-cost modelling, which determines the most efficient route assuming full knowledge of the environment, to investigate whether chimpanzees (Pan troglodytes) living in a rugged, montane environment walk least-cost routes to out of sight goals. We compared the ‘costs’ and geometry of observed movements with predicted least-cost routes and local knowledge (agent-based) and straight-line null models.  The least-cost model performed better than the local knowledge and straight-line models across all parameters, and linear mixed modelling showed a strong relationship between the cost of observed chimpanzee travel and least-cost routes.  Our study provides the first example of the ability to take least-cost routes to out of sight goals by chimpanzees and suggests they have spatial memory of their home range landscape. This ability may be a key trait that has enabled chimpanzees to maintain their energy balance in a low-resource environment.  Our findings provide a further example of how the advanced cognitive complexity of hominins may have facilitated their adaptation to a variety of environmental conditions and lead us to hypothesise that landscape complexity may play a role in shaping cognition.