The LHC experiments discovered a new particle of mass around 125 GeV, candidate for the scalar Higgs boson of the Standard Model. An e+e- collider operating close to the ZH threshold could be the tool of choice for studying this unique particle in detail. We present here the concept of a storage ring collider, which we call LEP3. Preliminary studies show that at a centre-of-mass energy of 240 GeV, near-constant luminosities of 10^34 cm^{-2}s^{-1} are possible in up to four collision points, while respecting a number of constraints including beamstrahlung. The integrated luminosity is 100fb^{-1}/y per interaction point, 20,000 e+e- --> ZH events would be produced per year and per experiment. LEP3 could also operate in multi-bunch mode at the Z resonance, with luminosities of several imes10^35 cm^{-2}s^{-1}, yielding O(10^11) Z decays per year, as well as just above the WW threshold. The short luminosity lifetime requires the use of top-up injection, which, in turn calls for a full-energy injector. The present design uses two rings (as in the BBbar factories): a low-emittance collider storage ring operating at a constant energy, and a separate "accelerator" ring that tops up the collider every few minutes. The LHeC lattice design has been used as a basis for our studies. Maximum luminosity is achieved with four bunches per beam. The estimated beam lifetime is about 8 minutes. The synchrotron radiation losses are 50 MW per beam. Further optimization of the design is possible. LEP3 could be installed in the LHC tunnel, serving ATLAS and CMS, and possibly up to two dedicated ILC-type detectors. Alternatively, could be installed in a new, longer tunnel of 80km, a machine operating up to the ttbar threshold. A number of basic questions about LEP3 are discussed and we have tried to identify the areas where R&D; will be needed. We consider the concept to be highly interesting and deserving of a detailed study.