  We analyze the extreme high-magnification microlensing event
OGLE-2008-BLG-279, which peaked at a maximum magnification of A ~ 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
+/- 0.10 M_Sun, and its distance, D_l = 4.0 +/- 0.6. 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_Earth ~= 2 M_Mars with projected separations near
the Einstein ring (~3 AU).
