  We report on observations of TeV-selected AGN made during the first 5.5
months of observations with the Large Area Telescope (LAT) on-board the Fermi
Gamma-ray Space Telescope (Fermi). In total, 96 AGN were selected for study,
each being either (i) a source detected at TeV energies (28 sources) or (ii) an
object that has been studied with TeV instruments and for which an upper-limit
has been reported (68 objects). The Fermi observations show clear detections of
38 of these TeV-selected objects, of which 21 are joint GeV-TeV sources and 29
were not in the third EGRET catalog. For each of the 38 Fermi-detected sources,
spectra and light curves are presented. Most can be described with a power law
of spectral index harder than 2.0, with a spectral break generally required to
accommodate the TeV measurements. Based on an extrapolation of the Fermi
spectrum, we identify sources, not previously detected at TeV energies, which
are promising targets for TeV instruments. Evidence for systematic evolution of
the $\gamma$-ray spectrum with redshift is presented and discussed in the
context of interaction with the EBL.
