Chebotarev's theorem describes statistically the decomposition behavior of primes in a Galois extension of algebraic number fields. This theorem was one of the cornerstones in the development of class field theory, and has since been generalized by Serre and others to describe the splitting of closed points in arithmetic schemes and varieties over finite fields. . In my talk, I will give a different 'generalization' to describe the asymtotic decomposition behavior of prime divisors in étale covers of projective varieties over arbitrary fields, and I will explain some applications.