Elastic scattering of antiprotons off ^{4}He, ^{12}C, and ^{16,18}O is described for the first time with a consistent microscopic approach based on the calculation of an optical potential (OP) describing the antiproton-target interaction. The OP is derived using the recent antiproton-nucleon (p[over ¯]N) chiral interaction to calculate the p[over ¯]N t matrix, while the target densities are computed with the ab initio no-core shell model using chiral interactions as well. Our results are in good agreement with the existing experimental data and the results computed at different chiral orders of the p[over ¯]N interaction display a well-defined convergence pattern.