The neologism "hadrontherapy" means radiotherapy with hadrons, which are the particles constituted by quarks, such as protons, neutrons and ions. The theoretical considerations about the clinical advantages this treatment modality can yield and the results obtained at the centers where it has already been used justify the proposal to project a center of this kind also in our Country. To this purpose, two of the authors of this paper (U. Amaldi, G. Tosi) founded the TERA Group formed by physicists, engineers and radiotherapists who work in close collaboration on a feasibility study for a hadrontherapy facility. The first aim of the Hadrontherapy Project is to design a center equipped with a synchrotron which, at the beginning, will accelerate negative hydrogen ions (H-) which will first produce 70-250 MeV proton beams and, then accelerate light ions (up to 16O) to 430 MeV/amu. This accelerator will serve four or five treatment rooms where patients can be irradiated simultaneously. Two rooms will be equipped with a fixed horizontal beam for the treatment of eye, head and neck tumors; the others will be equipped with rotating gantries to administer, in any clinical situation, really adequate treatment. Such a unit, when enough experience is fained, will allow at least 1000 patients to be treated yearly. The synchrotron injector will be designed so as to allow, parallel to the radiotherapy activities, other applications of medical and biological interest such as: the production of radioisotopes for diagnostic use (especially positron emitters), the analysis of trace elements through the PIXE technique and the production of thermal and epithermal neutrons for boron neutron capture therapy.