Monochromatic imaging in the nebular lines H alpha, H beta, [O III] lambda 5007, and [N II] lambda 6584 has been performed on 77 H II regions from 0.13R(eff) to 2.04R(eff) in the barred spiral galaxy NGC 3359. The galaxy shows several bright H II regions along its bar; according to numerical simulations of barred galaxies, this morphology suggests that the barred structure was formed recently (within 1 Gyr). The O/H abundance gradient across the disk of NGC 3359 was derived from the abundance indicators [O III]/H beta and [N II]/[O III] calibrated by Edmunds & Pagel (1984). A break in the slope of the O/H gradient is clearly seen near the corotation radius (similar to 4 kpc). The inner O/H gradient is steep [Delta log (O/H)/Delta R = -0.070 +/- 0.010 dex kpc(-1)] and the O/H scatter is moderate (+/- 0.10 dex); outside the corotation, the gradient appears flat [Delta log(O/H)/Delta R = 0.006 +/- 0.018 dex kpc(-1)] and the spread in O/H is significantly larger (+/- 0.2 dex) than in the inner parts. This result is in agreement with recent simulations of barred spiral galaxies: star formation inside the corotation radius is enhanced by large amounts of gas driven by radial flows induced by the bar and contributes to maintain the initial O/H gradient; in the outer parts, strong gas mixing induced by flows directed outward and along the spiral arms produces a flattened gradient (e.g., Friedli, Bent, and Kennicutt 1994). Based on previous H I kinematics data on NGC 3359 and results of numerical models of barred galaxies, we show that flows along the spiral arms have had enough time to wiped out the O/H gradient outside the corotation as far as at least 9.5 kpc. However, the presence of large azimuthal abundance fluctuations in the outer disk indicates that the age of the bar is similar to 4 x 10(8) yr. The steep inner O/H gradient is also discussed, and we suggest that the present star formation inside the corotation minimizes the dilution of the chemical composition by gas flows. Finally, a brief analysis of the global O/H gradients in disk galaxies with bars showing different star-forming activity is performed.