Interaction of a frequency-chirped laser pulse with single protons and a hydrogen gas target is studied analytically and by means of particle-in-cell simulations, respectively. The feasibility of generating ultraintense (10(7) particles per bunch) and phase-space collimated beams of protons (energy spread of about 1%) is demonstrated. Phase synchronization of the protons and the laser field, guaranteed by the appropriate chirping of the laser pulse, allows the particles to gain sufficient kinetic energy (around 250 MeV) required for such applications as hadron cancer therapy, from state-of-the-art laser systems of intensities of the order of 10(21) W/cm(2).