The properties of the – presumably – youngest Galactic supernova remnant ( SNR ) G1.9+0.3 are investigated within the framework of nonlinear kinetic theory of cosmic ray acceleration in SNRs . The observed angular size and expansion speed as well as the radio and X-ray emission measurements are used to determine relevant physical parameters of this SNR . Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova near the Galactic center ( at the distance d = 8.5 kpc ) the nonthermal properties are calculated . In particular , the expected TeV gamma-ray spectral energy density is predicted to be as low as \epsilon _ { \gamma } F _ { \gamma } \approx 5 \times 10 ^ { -15 } erg cm ^ { -2 } s ^ { -1 } , strongly dependent ( F _ { \gamma } \propto d ^ { -11 } ) upon the source distance d .