The linear polarization of x rays produced by dielectronic recombination into highly charged xenon ions was measured at an electron beam ion trap using the Compton polarimetry technique. This opens numerous possibilities for diagnostics of anisotropies of hot plasmas. Moreover, it was observed that the polarization of x rays, following the dielectronic capture populating the ${[1s2{s}^{2}2{p}_{1/2}]}_{1}$ state, is highly sensitive to the Breit interaction. The experimental results for this transition rule out by $5$σ${}$ calculations not taking the Breit interaction into account.