A number of panel unit root tests that allow for cross-section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross-dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard augmented Dickey-Fuller (ADF) regressions are augmented with the cross-section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual cross-sectionally augmented ADF (CADF) statistics and for their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.