  We present an exact one-loop calculation of the tunneling process in
Euclidean quantum gravity describing creation of black hole pairs in a de
Sitter universe. Such processes are mediated by $S^2\times S^2$ gravitational
instantons giving an imaginary contribution to the partition function. The
required energy is provided by the expansion of the universe. We utilize the
thermal properties of de Sitter space to describe the process as the decay of a
metastable thermal state. Within the Euclidean path integral approach to
gravity, we explicitly determine the spectra of the fluctuation operators,
exactly calculate the one-loop fluctuation determinants in the $\zeta$-function
regularization scheme, and check the agreement with the expected scaling
behaviour. Our results show a constant volume density of created black holes at
late times, and a very strong suppression of the nucleation rate for small
values of $\Lambda$.
