  Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over
an imaginary quadratic field F. In this paper, we prove an exceptional zero
conjecture in the case where f is new at a prime above p. More precisely, for
each prime $\mathfrak{p}$ of F above p we prove the existence of an L-invariant
$\mathcal{L}_{\mathfrak{p}}$, depending only on $\mathfrak{p}$ and f, such that
when the p-adic L-function of f has an exceptional zero at $\mathfrak{p}$, its
derivative can be related to the classical L-value multiplied by
$\mathcal{L}_{\mathfrak{p}}$. The proof uses cohomological methods of Darmon
and Orton, who proved similar results for GL(2) over the rationals. When p is
not split and f is the base-change of a classical modular form F, we relate
$\mathcal{L}_{\mathfrak{p}}$ to the L-invariant of F, resolving a conjecture of
Trifkovi\'{c} in this case.
