This paper proposes a fully nonparametric kernel method to account for observed covariates in regression discontinuity designs (RDD), which may increase precision of treatment effect estimation. It is shown that conditioning on covariates reduces the asymptotic variance and allows estimating the treatment effect at the rate of one-dimensional nonparametric regression, irrespective of the dimension of the continuously distributed elements in the conditioning set. Furthermore, the proposed method may decrease bias and restore identification by controlling for discontinuities in the covariate distribution at the discontinuity threshold, provided that all relevant discontinuously distributed variables are controlled for. To illustrate the estimation approach and its properties, we provide a simulation study and an empirical application to an Austrian labor market reform.