  In this Letter, we measure the full orbital architecture of the two-planet
system around the nearby K0 dwarf 14 Herculis. 14 Her (HD 145675, HIP 79248) is
a middle-aged ($4.6^{+3.8}_{-1.3}$ Gyr) K0 star with two eccentric giant
planets identified in the literature from radial velocity (RV) variability and
long-term trends. Using archival RV data from Keck/HIRES in concert with
\textit{Gaia-Hipparcos} acceleration in the proper motion vector for the star,
we have disentangled the mass and inclination of the b planet to
${9.1}_{-1.1}^{+1.0}$ $M_\mathrm{Jup}$ and ${32.7}_{-3.2}^{+5.3}$ degrees.
Despite only partial phase coverage for the c planet's orbit, we are able to
constrain its mass and orbital parameters as well to ${6.9}_{-1.0}^{+1.7}$
$M_\mathrm{Jup}$ and ${101}_{-33}^{+31}$ degrees. We find that coplanarity of
the b and c orbits is strongly disfavored. Combined with the age of the system
and the comparable masses of its planets, this suggests that planet-planet
scattering may be responsible for the current configuration of the system.
