The existence of chaos among the jovian planets is a contested issue. There exists both apparently unassailable evidence that the outer Solar System is chaotic, and that it is not. The discrepancy is particularly disturbing given that computed chaos is sometimes due to numerical artefacts. Here, we discount the possibility of numerical artefacts and demonstrate that the discrepancy seen between various investigators is real. It is caused by observational uncertainty in the orbital positions of the jovian planets, which is currently a few parts in 10million. Within that observational uncertainty, there exist clearly chaotic trajectories with complex structure and Lyapunov times-the timescale for the onset of chaos-ranging from 2million years to 230million years, as well as trajectories that show no evidence of chaos over 1Gyr timescales. Determining the true Lyapunov time of the outer Solar System will require a more accurate observational determination of the orbits of the jovian planets. A full understanding of the nature and consequences of the chaos may require further theoretical development.