How evolutionary changes in body size are brought about by variance in developmental timing and/or growth rates (also known as heterochrony) is a topic of considerable interest in evolutionary biology. In particular, extreme size change leading to gigantism occurred within the dinosaurs on multiple occasions. Whether this change was brought about by accelerated growth, delayed maturity or a combination of both processes is unknown. A better understanding of relationships between non-avian dinosaur groups and the newfound capacity to reconstruct their growth curves make it possible to address these questions quantitatively. Here we study growth patterns within the Tyrannosauridae, the best known group of large carnivorous dinosaurs, and determine the developmental means by which Tyrannosaurus rex, weighing 5,000kg and more, grew to be one of the most enormous terrestrial carnivorous animals ever. T. rex had a maximal growth rate of 2.1kgd-1, reached skeletal maturity in two decades and lived for up to 28 years. T. rex's great stature was primarily attained by accelerating growth rates beyond that of its closest relatives.