We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, which we call Markov Chain Beam Randomization, MCBR, ra
ndomly samples from a set of templates or functions that describe the beam uncertainties. The method is much faster than direct numerical integration over systematic `nuisance parameters, and is not restricted to simple, idealized cases as is analytic marginalization. It does not assume the data are normally distributed, and does not require Gaussian priors on the specific systematic uncertainties. We show that MCBR properly accounts for and provides the marginalized errors of the parameters. The method can be generalized and used to propagate any systematic uncertainties for which a set of templates is available. We apply the method to the Planck satellite, and consider future experiments. Beam measurement errors should have a small effect on cosmological parameters as long as the beam fitting is performed after removal of 1/f noise.
