Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction1, 2 of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics3, 4, 5, 6, 7, 8. However, the observation of Efimov quantum states has remained an elusive goal3, 5. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss9, 10 when the strength of the two-body interaction is varied. We also detect a minimum9, 11, 12 in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems7. While Feshbach resonances13, 14 have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter15 to the world of few-body quantum phenomena.