The Eocene (55-34 Mya) was marked by a transition from a greenhouse to an icehouse climate, and also experienced several hyperthermals, which are rapid, extreme global warming events. These hyperthermal events were caused by rapid increases in atmospheric CO₂ concentration, so they provide the opportunity to study how Earth systems respond to rapid and high magnitude changes in atmospheric CO₂. Understanding the drivers of major climate change events, like these ones, is an important step in understanding modern climate change. One such event, the Middle Eocene Climatic Optimum, was a major climatic shift lasting approximately 500 kyr. Orbital forcers, most notably variations in the amount of solar irradiance reaching Earth, are believed to explain many of the observed climatic variations in both this epoch and others. Changes in orbital patterns are widely believed to explain cyclicities on the 20,000 to 100,000 year scale, while changes in solar irradiance have effects on the sub-1,000 year scale. However, little work has been done to understand the influence of orbital cycles of periods between these, in the millennial range. This study aims to bridge this knowledge gap by performing spectral analyses of Middle Eocene Climatic Optimum temperature proxy records to determine if millennial-range orbital cycles have an observable influence on climate dynamics. Using temperature proxy data from four Ocean Drilling Program sites, spectral analysis was performed and prominent signals in the spectra were identified. This analysis showed that all studied sites had a statistically significant signal in the 2500 ± 250-year range, which was identified as the Hallstatt cycle. A suggested mechanism for the Hallstatt cycle, a spin-orbit coupling of the Jovian planets, is astronomical in origin. This adds further evidence that dynamical solar system chaos during this period contributed to the abnormal climate patterns at play and suggests that external factors have a larger climate forcing ability than previously thought. Delving into the intricacies of solar system chaos and its impact on past climates enhances our understanding of present and future climates, thus empowering more accurate and informed predictions going forward.