  The {\it Kepler} mission has detected thousands of planetary systems with 1-7
transiting planets packed within 0.7~au from their host stars. There is an
apparent excess of single-transit planet systems that cannot be explained by
transit geometries alone, when a single planetary mutual inclination dispersion
is assumed. This suggests that the observed compact planetary systems have at
least two different architectures. We present a scenario where the "Kepler
dichotomy" may be explained by the action of an external giant planet or
stellar companion misaligned with the inner multi-planet system. The external
companion excites mutual inclinations of the inner planets, causing such
systems to appear as "Kepler singles" in transit surveys. We derive approximate
analytic expressions (in various limiting regimes), calibrated with numerical
calculations, for the mutual inclination excitations for various planetary
systems and perturber properties (mass $m_p$, semi-major axis $a_p$ and
inclination $\theta_p$). In general, the excited mutual inclination increases
with $m_p/a_p^3$ and $\theta_p$, although secular resonances may lead to large
mutual inclinations even for small $\theta_p$. We discuss the implications of
our results for understanding the dynamical history of transiting planet
systems with known external perturbers.
