Attention deficit hyperactivity disorder is a neurodevelopmental condition associated with varying levels of hyperactivity, inattention, and impulsivity. This study investigated brain function in children with attention deficit hyperactivity disorder using measures of nonlinear dynamics in electroencephalogram signals during rest. During eyes-closed resting, 19 channel electroencephalogram signals were recorded from 12 ADHD and 12 normal age-matched children. The multifractal singularity spectrum, the largest Lyapunov exponent, and approximate entropy were employed to quantify the chaotic nonlinear dynamics of these electroencephalogram signals. As confirmed by Wilcoxon rank sum test, the largest Lyapunov exponent over left frontal-central cortex exhibited a significant difference between attention deficit hyperactivity disorder subjects and the age-matched control groups. Further, mean approximate entropy was significantly lower in attention deficit hyperactivity disorder subjects in prefrontal cortex. The singularity spectrum was also considerably altered in attention deficit hyperactivity disorder subjects when compared to control children. Evaluation of these features was performed with two classifiers: a support vector machine and a radial basis function neural network. For better comparison, subject classification based on frequency band power was assessed using the same types of classifiers. Nonlinear features provided better discrimination between attention deficit hyperactivity disorder and control than band power features. Under four-fold cross-validation testing, the support vector machine gave 83.33% accurate classification results.