A crossed beam experiment has been used to measure absolute charge capture cross sections in collisions of slow highly charged xenon ions with laser excited Rydberg atoms. The cross sections were measured for scaled projectile velocities nv" from 1.0 to 6.0, for projectile charges of 8, 16, 32, and 40, where n is the principal quantum number of the target electron. Experimental cross sections are compared with predictions of classical models.PACS number(s): 34.60.+z, 34.70.+e A substantial amount of work has been done investigating charge capture cross sections, both difFerential [1,2] and total [3] in final principal quantum number, for singly charged projectiles incident on target Rydberg atoms. This work has recently been supplemented by studies using Rydberg targets that have been put into circular [4] and elliptical [5] states. None of the above cross sections are absolute. On the theoretical side, while some progress is being made in quantum mechanical calculations [6] through the use of propensity rules, to date, only classical treatments, such as classical trajectory Monte Carlo (CTMC) calculations [7] or the Bohr-Lindhard model [8], are capable of producing predictions of cross sections for these collisions. In order to test the validity of classical calculations, as well as to provide test cases for future quantum mechanical calculations, it is of great current interest to have absolute cross sections for charge capture with Rydberg targets, which are differential in as many parameters as possible, including the projectile charge state. In this work we report absolute charge capture cross sections measured. for the collision system of Xe~+ + Rb(10 f), for q = 8, 16, 32, 40, and for scaled pro-jectile velocities vz/v, between 1.0 and 6.0, where v, is