Nanoscale systems are the subject of forefront interdisciplinary research. The underlying physics renders dynamics of nanosystems nonlinear. Despite extensive research on chaotic dynamics in low-dimensional dynamical systems, little has been done for nanoscale systems. Due to the potentially widespread use of nanoscale systems in science, engineering, and technological applications, it is imperative to investigate and exploit nonlinear dynamics in such systems. This paper addresses this fundamental topic by investigating a prototypical class of nanoelectromechanical systems (NEMS): electrostatically driven Si-nanowires. We find that multistability and complicated structures of basin of attraction are common, and the latter can be attributed to high-dimensional transient chaos. Implications of these phenomena to device operations are explored.