The connection between brain rhythms at rest and cognition remains poorly understood. This is especially true during early childhood in which neuroimaging data are relatively scarce. We developed a new method for collecting eyes closed and eyes open resting state electroencephalography (EEG) suitable for young children. We report results characterizing age-related change in power in multiple brain rhythms over frontal and posterior regions under eyes closed and open conditions of rest in 3-, 4-, 5- and 9-year-old children (N = 162). We observed two key patterns of results. First, with age theta decreased, alpha increased, and alpha peak frequency increased. Second, power was generally higher when eyes were closed than open for theta and alpha but higher when eyes were open than closed for beta and gamma. We also investigated the relation between resting state EEG activity and executive function (EF) using the Minnesota Executive Function Scale, a standardized behavioral measure of EF for ages 2 and up. Correlational and regression analyses showed that individual differences in the theta/beta ratio is associated with EF even after controlling for children's age and verbal abilities. We situate our results in a theoretical discussion of theta/beta and its role in control processes.