We report the discovery of a \sim 3 \degr \hbox to 0.0 pt { . } 4 -wide region of high-energy emission in data from the Fermi LAT satellite . The centroid of the emission is located in the Southern Hemisphere sky , a few degrees away from the plane of the Galaxy at the Galactic coordinates l=350 \degr \hbox to 0.0 pt { . } 6 , b=-4 \degr \hbox to 0.0 pt { . } 7 . It shows a hard spectrum that is compatible with a simple power-law , \frac { dN } { dE } \propto E ^ { - \Gamma } , in the energy range 0.7–500 GeV , with a spectral index \Gamma = 1.68 \pm 0.04 _ { \mbox { \tiny stat } } \pm 0.1 _ { \mbox { \tiny sys } } . The integrated source photon flux above 0.7 GeV is ( 4.71 \pm 0.49 _ { \mbox { \tiny stat } } \pm 2.13 _ { \mbox { \tiny sys } } ) \times 10 ^ { -9 } cm ^ { -2 } s ^ { -1 } . We discuss several hypotheses for the nature of the source , particularly that the emission comes from the shell of an unknown supernova remnant .