In 1975, John Rex Beddington, C. A. Free and John Lawton proposed a map governing two interacting populations, preys and predators : 
where xn designates the preys and yn the predators. This two-dimensional discrete map considers populations with non-overlapping generations and was based on Nicholson-Bailey host-parasite equations to describe the interactions between a population of herbivorous arthropods --- invertebrate animal having an exoskeleton --- and their insect parasitoïds.  Beddington and coworkers observed some chaotic behaviors as the one plotted in Fig. 1 with the parameter values
This map is most likely one of the very first to be chaotic and published.
 J. R. Beddington, C. A. Free & J. H. Lawton, Dynamic complexity in predator-prey models framed in difference equations, Nature, 255, 58-60, 1975. Online
 A. J. Nicholson & V. A. Bailey, The balance of animal populations, Proceedings of the Zoological Society of London, 105 (3), 551-598, 1935. Online