Granger causality has traditionally been studied under the assumption of a linear vector autoregressive (VAR) model, with tests focusing on the significance of the VAR coefficients. We address the problem of testing a model-free null hypothesis of conditional independence in time series—specifically, whether $Y_{t+1}$ and $X_t$ are conditionally independent given the history of $Y$ up to time $t$. We propose nonlinearly regressing both of them on the history of $Y$ up to time $t$, and calculating a test statistic based on the sample covariance of residuals, called the Generalized Temporal Covariance Measure (GTCM). The type I error control of the test relies on the relatively weak assumption that user-chosen regression procedures estimate conditional means at a sufficiently fast rate that is slow enough to accommodate nonparametric settings. By further assuming stability of the regression procedures and weak dependence in the time series, we can utilize the entire dataset to estimate the conditional means without splitting the time series into subsets.