We provide a new solution to the long-standing problem of inferring causality from observations without modeling the unknown mechanisms. We show that the evolution of any dynamical system is related to a predictive asymmetry that quantifies causal connections from limited observations. A built-in significance criterion obviates surrogate testing and drastically improves computational efficiency. We validate our test on numerous synthetic systems exhibiting behavior commonly occurring in nature, from linear and nonlinear stochastic processes to systems exhibiting non-linear deterministic chaos, and on real-world data with known ground truths. Applied to the controversial problem of glacial-interglacial sea level and CO2 evolving in lock-step, our test uncovers empirical evidence for CO2 as a driver of sea level over the last 800 thousand years. Our findings are relevant to any discipline where time series are used to study natural systems.