AbstractThis talk covers preliminary work in which we apply a strictly differential line-by-line chemical abundance analysis to high quality UVES spectra of the globular cluster NGC 6752. We achieve extremely high precision in the measurement of relative abundance ratios. Our results indicate that the observed abundance dispersion exceeds the measurement uncertainties and that many pairs of elements show significant correlations when plotting [X1/H] vs. [X2/H]. Our tentative conclusions are that either NGC 6752 is not chemically homogeneous at the ≃0.03 dex level or the abundance variations and correlations signify star-to-star He abundance variations.