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Periodic fluctuations in past biodiversity, speciation, and extinction have been proposed, with extremely long periods ranging from 26 to 62 million years, although forcing mechanisms remain speculative. In contrast, well-understood periodic Milankovitch climate forcing represents a viable driver for macroevolutionary fluctuations, although little evidence for such fluctuation exists except during the Late Cenozoic. The reality, magnitude, and drivers of periodic fluctuations in macroevolutionary rates are of interest given long-standing debate surrounding the relative roles of intrinsic biotic interactions vs. extrinsic environmental factors as drivers of biodiversity change. Here, we show that, over a time span of 60 million years, between 9 and 16% of the variance in biological turnover (i.e., speciation probability plus species extinction probability) in a major Early Paleozoic zooplankton group, the graptoloids, can be explained by long-period astronomical cycles (Milankovitch "grand cycles") associated with Earth's orbital eccentricity (2.6 million years) and obliquity (1.3 million years). These grand cycles modulate climate variability, alternating times of relative stability in the environment with times of maximum volatility. We infer that these cycles influenced graptolite speciation and extinction through climate-driven changes to oceanic circulation and structure. Our results confirm the existence of Milankovitch grand cycles in the Early Paleozoic Era and show that known processes related to the mechanics of the Solar System were shaping marine macroevolutionary rates comparatively early in the history of complex life. We present an application of hidden Markov models to macroevolutionary time series and protocols for the evaluation of statistical significance in spectral analysis.