  Triple symbols are arithmetic analogues of the mod $n$ triple linking number
in topology, where $n > 1$ is an integer. In this paper, we introduce a
cohomological formulation of a mod $n$ triple symbol for characters over a
number field containing a primitive $n$-th root of unity. Our definition is
motivated by the arithmetic Chern--Simons theory and in this respect it differs
from earlier approaches to triple symbols. We show that our symbol agrees with
that of R\'edei when $n=2$ and of Amano--Mizusawa--Morishita when $n=3$.
