The production of charmed particles by Sigma- of 340 Gev/c momentum was studied in the hyperon beam experiment WA89 at the CERN-SPS, using the Omega-spectrometer. In two data-taking periods in 1993 and 1994 an integrated luminosity of 1600 microb^-1 on copper and carbon targets was recorded. From the reconstruction of 930 +- 90 charm particle decays in 10 decay channels production cross sections for D, antiD, Ds and Lambdac were determined in the region xF>0. Assuming an A^1 dependence of the cross section on the nucleon number, we calculate a total ccbar production cross section of sigma(x_F > 0) = 5.3+- 0.4(stat)+-1.0(syst)+1.0(Xi_c) microb per nucleon. The last term is an upper limit on the unknown contribution from charmed-strange baryon production.