Summary: We give an estimate on the conservation error due to the non-conservative data interpolation scheme for overset grids. It is shown that the conservation error is a first-order term if second-order conservative schemes are employed for Chimera grids and if discontinuities are located away from overlapped grid interfaces. Therefore, in the limit of global grid refinement, valid numerical solutions should be obtained with a data interpolation scheme. In one demonstration case the conservation error in the original Chimera scheme was shown to affect flow even without discontinuities on coarse to medium grids. The conservative Chimera scheme was shown to give significantly better solutions than the original Chimera scheme on these grids with other factors being the same.