Any infinitely divisible distribution on $R^n$ with infinite absolutely continuous Levy measure and no Gaussian component has a density which is positive a.e. over its support.
@article{1176996363,
author = {Hudson, W. N. and Mason, J. D.},
title = {More on Equivalence of Infinitely Divisible Distributions},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 563-568},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996363}
}
Hudson, W. N.; Mason, J. D. More on Equivalence of Infinitely Divisible Distributions. Ann. Probab., Tome 3 (1975) no. 6, pp. 563-568. http://gdmltest.u-ga.fr/item/1176996363/