We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279 , which peaked at a maximum magnification of A \sim 1600 on 30 May 2008 . The peak of this event exhibits both finite-source effects and terrestrial parallax , from which we determine the mass of the lens , M _ { l } = 0.64 \pm 0.10 M _ { \odot } , and its distance , D _ { l } = 4.0 \pm 0.6 \mathrm { kpc } . We rule out Jupiter-mass planetary companions to the lens star for projected separations in the range 0.5-20 AU . More generally , we find that this event was sensitive to planets with masses as small as 0.2 ~ { } M _ { \oplus } \simeq 2 ~ { } M _ { Mars } with projected separations near the Einstein ring ( \sim 3 ~ { } { AU } ) .