Scalar polynomial systems with time delays are an important class in delay systems. In practical applications, many models are described by scalar polynomial time-delay systems. Additionally, from a mathematical point of view, smooth delay systems can be locally approximated as polynomial delay systems through Taylor expansions. By neglecting higher-order terms, local bifurcations of nonlinear delay systems can be investigated by analyzing these approximated polynomial delay systems. Therefore, scalar polynomial time-delay systems can be regarded as a prototype for studying other delay systems, making the study of polynomial delay systems crucial. In this paper, we investigate a class of scalar quartic polynomial delay systems. We discovered rich chaotic dynamics in this system through numerical simulation. Moreover, this chaotic quartic system may serve as an approximation, via Taylor expansion, for a wide class of scalar delay differential equations. As a result, these nonlinear systems may exhibit chaotic behaviors, and our study may provide an insight into the emergence of chaos in other time-delay nonlinear systems.