The exploration of the Jovian System and its fascinating satellite Europa is one of the priorities presented in ESA’s “Cosmic Vision” strategic document. The Jovian System indeed displays many facets. It is a small planetary system in its own right, built-up out of the mixture of gas and icy material that was present in the external region of the solar nebula. Through a complex history of accretion, internal differentiation and dynamic interaction, a very unique satellite system formed, in which three of the four Galilean satellites are locked in the so-called Laplace resonance. The energy and angular momentum they exchange among themselves and with Jupiter contribute to various degrees to the internal heating sources of the satellites. Unique among these satellites, Europa is believed to shelter an ocean between its geodynamically active icy crust and its silicate mantle, one where the main conditions for habitability may be fulfilled. For this very reason, Europa is one of the best candidates for the search for life in our Solar System. So, is Europa really habitable, representing a “habitable zone” in the Jupiter system? To answer this specific question, we need a dedicated mission to Europa. But to understand in a more generic way the habitability conditions around giant planets, we need to go beyond Europa itself and address two more general questions at the scale of the Jupiter system: to what extent is its possible habitability related to the initial conditions and formation scenario of the Jovian satellites? To what extent is it due to the way the Jupiter system works? ESA’s Cosmic Vision programme offers an ideal and timely framework to address these three key questions. Building on the in-depth reconnaissance of the Jupiter System by Galileo (and the Voyager, Ulysses, Cassini and New Horizons fly-by’s) and on the anticipated accomplishments of NASA’s JUNO mission, it is now time to design and fly a new mission which will focus on these three major questions. LAPLACE, as we propose to call it, will deploy in the Jovian system a triad of orbiting platforms to perform coordinated observations of its main components: Europa, our priority target, the Jovian satellites, Jupiter’s magnetosphere and its atmosphere and interior. LAPLACE will consolidate Europe’s role and visibility in the exploration of the Solar System and will foster the development of technologies for the exploration of deep space in Europe. Its multi-platform and multi-target architecture, combined with its broadly multidisciplinary scientific dimension, will provide an outstanding opportunity to build a broad international collaboration with all interested nations and space agencies.