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 \pm 0.7 _ { \mathrm { stat } } \pm 0.2 _ { \mathrm { syst } } . The integral flux above 180 GeV is ( 3.9 \pm 0.8 _ { \mathrm { stat } } \pm 1.0 _ { \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 .