First results from a new UV laser ablation MC-ICPMS method for measuring Mg isotope ratios in situ in meteoritical materials show that there are mass-dependent variations in δ25Mg and δ26Mg up to 1.5 ‰ per amu in chondrules and 0.3‰ per amu in a CAI from the Allende meteorite. In both cases the mass-dependent fractionation is associated with alteration. Comparisons with laser ablation O isotope data indicate that incorporation of pre-existing grains of forsterite with distinct Mg and O isotopic compositions and post-formation alteration both contributed to the variability in Mg isotope ratios in the chondrules, resulting in a correlation between high δ25Mg and low Δ17O. The laser ablation analyses of the CAI show that high-precision determinations of both δ25Mg and δ26Mg can be used to discriminate features of the 26Al-26Mg isotope system that are relevant to chronology from those that result from element mobility.