  We present 11.2 micron observations of the gravitationally lensed, radio-loud
z_s=2.64 quasar MG0414+0534, obtained using the Michelle camera on Gemini
North. We find a flux ratio anomaly of A2/A1= 0.93 +/- 0.02 for the quasar
images A1 and A2. When combined with the 11.7 micron measurements from Minezaki
et al. (2009), the A2/A1 flux ratio is nearly 5-sigma from the expected ratio
for a model based on the two visible lens galaxies. The mid-IR flux ratio
anomaly can be explained by a satellite (substructure), 0.3" Northeast of image
A2, as can the detailed VLBI structures of the jet produced by the quasar. When
we combine the mid-IR flux ratios with high-resolution VLBI measurements, we
find a best-fit mass between 10^(6.2) and 10^(7.5) M_sol inside the Einstein
radius for a satellite substructure modeled as a singular isothermal sphere at
the redshift of the main lens (z_l=0.96). We are unable to set an interesting
limit on the mass to light ratio due to its proximity to the quasar image A2.
While the observations used here were technically difficult, surveys of flux
anomalies in gravitational lenses with the James Webb Space Telescope will be
simple, fast, and should well constrain the abundance of substructure in dark
matter haloes.
