Abstract: In a planetary system with well-spaced planets, there is a nonlinear instability that can lead to chaotic behaviour. One of the planets can gradually become unstable, in which case its orbit becomes highly eccentric. This "secular chaos" is known to be responsible for the eventual destabilization of Mercury in our own Solar System. Here I focus on systems with multiple giant planets. I show that after an extended period of eccentricity diffusion, the inner planet's pericentre can approach the star to within a few stellar radii. Strong tidal interactions with the star then pull the planet inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which I term "secular migration") explains a range of observations: the pile-up of hot Jupiters at 3-day orbital periods, the fact that hot Jupiters are in general less massive than other RV planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). I will also show that if an unstable planet escapes the influence of the other planets, the remaining planetary system becomes increasingly stable. This may explain the stable architecture of observed systems.