Measurement of D+ and Lambda_c+ production in deep inelastic scattering at HERA ZEUS Collaboration Abstract Charm production in deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 120 pb-1. The hadronic decay channels D+ -> K0S pi+, Lambda_c+ -> p K0S and Lambda_c+ -> Lambda pi+, and their charge conjugates, were reconstructed. The presence of a neutral strange hadron in the final state reduces the combinatorial background and extends the measured sensitivity into the low transverse momentum region. The kinematic range is 0 < pT(D+,Lambda_c+) < 10GeV, |eta(D+,Lambda_c+)| < 1.6, 1.5 < Q2 < 1000GeV2 and 0.02 < y < 0.7. Inclusive and differential cross sections for the production of D+ mesons are compared to next-to-leading-order QCD predictions. The fraction of c quarks hadronising into Lambda_c+ baryons is extracted.