  We present results from multiwavelength observations of the BL Lacertae
object 1ES 1741+196, including results in the very-high-energy $\gamma$-ray
regime using the Very Energetic Radiation Imaging Telescope Array System
(VERITAS). The VERITAS time-averaged spectrum, measured above 180 GeV, is
well-modelled by a power law with a spectral index of
$2.7\pm0.7_{\mathrm{stat}}\pm0.2_{\mathrm{syst}}$. The integral flux above 180
GeV is $(3.9\pm0.8_{\mathrm{stat}}\pm1.0_{\mathrm{syst}})\times 10^{-8}$
m$^{-2}$ s$^{-1}$, corresponding to 1.6% of the Crab Nebula flux on average.
The multiwavelength spectral energy distribution of the source suggests that
1ES 1741+196 is an extreme-high-frequency-peaked BL Lacertae object. The
observations analysed in this paper extend over a period of six years, during
which time no strong flares were observed in any band. This analysis is
therefore one of the few characterizations of a blazar in a non-flaring state.
