We have mapped the edge-on galaxy NGC3628 in the 12CO(2−1) and 13CO(2−1) lines with the IRAM 30m MRT and in radio continuum at λ20 cm with the VLA. The 12CO(2−1) spectra were obtained out to a distance of 3 kpc east and 2 kpc west of the edge-on galaxy (resolution 0.4 kpc) with supplementary spectra ≃ 9 kpc east and west (1 arcmin ≃ 2 kpc at a distance of 6.7 Mpc). The resulting map shows a central peak of CO emission but also a multiple peaked structure from which we deduce a ringlike enhancement of molecular gas with a diameter of ≃ 400 pc and two outer maxima likely indicating spiral arms of the galaxy. The view of a molecular “ring” is supported by the fact that the maxima of the CO intensity are located close to the turnover radius where rigid rotation passes into differential rotation. Lesch et al. (1990) found for a number of galaxies with molecular rings that these rings can be formed by viscous accretion of molecular gas even at these radii. We find for the rigid rotating disk a molecular mass of m ≃ 108M⊙ assuming a conventional conversion factor. From our channelmaps we were able to distinguish between six unresolved clumps in the central region with comparable CO emissivity and masses of ≃ 106M⊙.