  We have measured pi+pi- and K+K- production in two-photon collisions using
87.7 /fb of data collected with the Belle detector at the asymmetric energy
e+e- collider KEKB. The cross sections are measured to high precision in the
two-photon center-of-mass energy (W) range between 2.4 GeV < W < 4.1 GeV and
angular region |cos theta^{*}| < 0.6. The cross section ratio
sigma(gammagamma->K+K-)/sigma(gammagamma->pi+pi-) is measured to be 0.89 +-
0.04(stat) +- 0.15(syst) in the range of 3.0 GeV < W < 4.1 GeV, where the ratio
is energy independent. We observe a sin^{-4} theta^{*} behavior of the cross
section in the same W range. Production of chi_{c0} and chi_{c2} mesons is
observed in both gammagamma -> pi+pi- and gammagamma -> K+K- modes.
