  We compute explicitly the normal zeta functions of the Heisenberg groups
$H(R)$, where $R$ is a compact discrete valuation ring of characteristic zero.
These zeta functions occur as Euler factors of normal zeta functions of
Heisenberg groups of the form $H(\mathcal{O}_K)$, where $\mathcal{O}_K$ is the
ring of integers of an arbitrary number field~$K$, at the rational primes which
are non-split in~$K$. We show that these local zeta functions satisfy
functional equations upon the inversion of the prime.
