MgCn (n = 1-7) open-chain clusters, as well as their cationic and anionic derivatives, have been studied by means of the B3LYP density functional method. Results for several molecular properties which could help in their possible experimental characterization, such as equilibrium geometries, electronic energies, dipole moments and vibrational frequencies, are provided. MgCn clusters are predicted to be linear with triplet ground states, with the only exception Of MgC2 that has a (1)Sigma ground state. Both cationic and anionic clusters have doublet ground states, except for the first members of the series, MgC+ and MgC-, which are found to have (4)Sigma ground states. The analysis of incremental binding energies shows that both MgCn and MgCn- species exhibit a clear even-odd alternation in stability, n-even clusters being always more stable than n-odd ones. This alternation is also reflected in the electron affinity values, which are higher for n-even clusters. In the case of the cationic clusters, the stability alternation is reversed along the series, and for larger MgCn+ species n-odd species seem to be more stable.