The MAGIC telescopes discovered very high energy (VHE, E>100 GeV) gamma-ray emission coming from the distant Flat Spectrum Radio Quasar (FSRQ) PKS 1222+21 (4C +21.35, z=0.432). It is the second most distant VHE gamma-ray source, with well measured redshift, detected until now. The detection coincides with high energy MeV/GeV gamma-ray activity measured by the Large Area Telescope (LAT) on board the Fermi satellite. The VHE and MeV/GeV spectra, corrected for the absorption by the extragalactic background light, can be described by a single power law with photon index 2.72 ± 0.34 between 3 GeV and 400 GeV, consistent with gamma-ray emission belonging to a single component in the jet. The absence of a spectral cutoff constrains the gamma-ray emission region to lie outside the Broad Line Region, which would otherwise absorb the VHE gamma-rays. On the other hand, the MAGIC measurement of a doubling time of about 9 minutes indicates an extremely compact emission region, in conflict with the "far dissipation" scenario. This result challenges jet emission models in FSRQs and indicates the importance of jet sub-structures.