Alysa Rogers Brandeis University Physics Department University of Wisconsin, Madison, Daniel Schwartz Center for Astrophysics | Harvard & Smithsonian, Cristiana Spingola Istituto di Radioastronomia, Bologna, Italy, Anna Barnacka Center for Astrophysics | Harvard & Smithsonian

Active galactic nuclei (AGN) are some of the most powerful objects in the Universe. For this reason, they can be observed up to high redshifts (z), giving valuable insights into the evolution of our Universe. However, high-z AGN are too distant to be spatially resolved with current or upcoming X-ray facilities. In this paper we show how we can exploit gravitationally lensed AGN to significantly increase spatial resolution even at high-z. We combine astrometric data from Gaia DR3 with imaging from the Chandra X-ray Observatory of the quadruply-lensed quasar HE 0435--1223 to measure for the first time possible offsets between the optical and the X-ray emissions. We measure the X-ray source position for HE 0435-1223 within a 1$\sigma$ quasi-elliptical region of 0.5 x 1.3 milli-arcsecond (mas), about 150 pc$^2$ at the redshift of the source (z=1.689). We find evidence for the X-ray emission being offset by a projected 3 mas from the Gaia (optical) emission. The positional offset is most likely associated to a portion of the X-ray emission arising from an X-ray jet or outflow. We also discuss how this method can be used to indicate the presence of a binary/offset AGN system.