This article considers testing for normality for time series data. In econometrics the typical testing procedure employs the Jarque-Bera test statistic, which has an asymptotic chi-square distribution when the considered series is uncorrelated. However, with time series data it often happens that the model is not correctly specified, and in other cases the researcher might not be interested in modeling the serial correlation. In these cases, the Jarque-Bera test is invalid because it does not take the serial correlation into account. In this paper we propose a simple nonparametric modification of the Jarque-Bera test that is robust to the presence of serial correlation of a general form. Besides its simplicity, the remarkable feature of our test is that it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.