  CTB 109 (G109.1-1.0) is a Galactic supernova remnant (SNR) with a
hemispherical shell morphology in X-rays and in the radio band. In this work we
report the detection of {\gamma}-ray emission coincident with CTB 109, using 37
months of data from the Large Area Telescope on board the Fermi Gamma-ray Space
Telescope. We study the broadband characteristics of the remnant using a model
that includes hydrodynamics, efficient cosmic ray acceleration, nonthermal
emission and a self-consistent calculation of the X-ray thermal emission. We
find that the observations can be successfully fit with two distinct parameter
sets, one where the {\gamma}-ray emission is produced primarily by leptons
accelerated at the SNR forward shock and the other where {\gamma}-rays produced
by forward shock accelerated cosmic-ray ions dominate the high-energy emission.
Consideration of thermal X-ray emission introduces a novel element to the
broadband fitting process, and while it does not rule out either the leptonic
or the hadronic scenarios, it constrains the parameter sets required by the
model to fit the observations. Moreover, the model which best fits the thermal
and nonthermal emission observations is an intermediate case, where both
radiation from accelerated electrons and hadrons contribute almost equally to
the {\gamma}-ray flux observed.
