"Key questions in particle and astroparticle physics can be answered only by construction of new giant underground observatories to search for rare events and to study sources of terrestrial and extra-terrestrial neutrinos. In this context, the European Astroparticle Roadmap of 03/07, via ApPEC and ASPERA, states: “We recommend a new large European infrastructure, an international multi-purpose facility of 105-106 ton scale for improved studies of proton decay and low-energy neutrinos. Water-Cherenkov, Liq. Scintillator & Liq. Argon should be evaluated as a common design study together with the underground infrastructure and eventual detection of accelerator neutrino beams. This study should take into account worldwide efforts and converge by 2010...” Furthermore, the latest particle physics roadmap from CERN of 11/06 states:“A range of very important non-accelerator experiments takes place at the overlap of particle and astroparticle physics exploring otherwise inaccessible phenomena; Council will seek with ApPEC a coordinated strategy in these areas of mutual interest.” Reacting to this, uniting scientists across Europe, we propose here a design study, LAGUNA, to produce by 2010 a full conceptual design sufficient to provide policy makers and funding agencies with enough information for a construction decision. Has Europe the technical and human capability to lead future underground science by hosting the next generation underground neutrino and rare event observatory? We aim to answer this question. Certainly construction will exceed the capacity of any single European nation - to compete with the US and Asia unification of our scattered efforts is essential. Failure to plan now risks not only that our picture of Nature's laws remain fundamentally incomplete but also that leadership in the field enjoyed by Europe for 20 years falls away. EU FP7 input now is timely and will have major strategic impact, guaranteeing coherence and stimulating national funding."