Geysers are systems that exhibit hydrothermal eruptive behavior at irregular and, occasionally, relatively regular intervals. Because geyser dynamics are governed by strongly nonlinear differential equations, it is reasonable to expect that these systems are capable of displaying chaotic behavior. Geyser dynamics are shown to be analogous to a simple conceptual model known to exhibit chaotic behavior. State space reconstructions of eruption interval data then show that the geyser Old Faithful erupts at chaotic intervals. Establishing the system as chaotic explains the inability to predict long-term eruptive behavior of Old Faithful.