Abstract: We report a measurement of the D-0 and D+ lifetimes using D-0 -> K-pi(+) and D+ -> K-pi(+)pi(+) decays reconstructed in e(+)e(-) -> c (c) over bar data recorded by the Belle II experiment at the SuperKEKB asymmetric-energy e(+)e(-) collider. The data, collected at center-of-mass energies at or near the (sic)(4S) resonance, correspond to an integrated luminosity of 72 fb(-1). The results, (tau)(D-0) = 410.5 +/- 1.1 (stat) +/- 0.8(syst) fs and tau(D-0) = 1030.4 +/- 4.7 (stat) +/- 3.1 (syst) fs, are the most precise to date and are consistent with previous determinations.