  Direct measurements of the extragalactic background light (EBL) in the
near-IR to mid-IR waveband are extremely difficult due to an overwhelming
foreground from the zodiacal light that outshines the faint cosmological
diffuse radiation field by more than an order of magnitude. Indirect
constraints on the EBL are provided by gamma-ray observations of AGN. Using the
combination of the Fermi Gamma-Ray Space Telescope together with the current
generation of ground-based air Cherenkov telescopes (H.E.S.S., MAGIC, and
VERITAS) provides unprecedented sensitivity and spectral coverage for
constraining the EBL in the near- to mid-IR. In this paper we present new
limits on the EBL based on the analysis of the broad-band spectra of a select
set of gamma-ray blazars covering 200 MeV to several TeV. The EBL intensity at
15 microns is constrained to be 1.36 +/- 0.58 nW m^-2 sr^-1. We find that the
fast evolution and baseline EBL models of Stecker et al. (2006), as well as the
model of Kneiske et al. (2004), predict significantly higher EBL intensities in
the mid-IR (15 microns) than is allowed by the constraints derived here. In
addition, the model of Franceschini et al. (2008) and the fiducial model of
Dominguez et al. (2011) predict near- to mid-IR ratios smaller than that
predicted by our analysis. Namely, their intensities in the near-IR are too low
while their intensities in the mid-IR are marginally too high. All of the
aforementioned models are inconsistent with our analysis at the >3 sigma level.
