We report the first detection of very-high-energy (VHE) gamma-ray emission above 140 GeV from PKS 1424+240, a BL Lac object with an unknown redshift. The photon spectrum above 140 GeV measured by VERITAS is well described by a power law with a photon index of 3.8 +- 0.5_stat +- 0.3_syst and a flux normalization at 200 GeV of (5.1 +- 0.9_stat +- 0.5_syst) x 10^{-11} TeV^-1 cm^-2 s^-1, where stat and syst denote the statistical and systematical uncertainty, respectively. The VHE flux is steady over the observation period between MJD 54881 and 55003 (2009 February 19 to June 21). Flux variability is also not observed in contemporaneous high energy observations with the Fermi Large Area Telescope (LAT). Contemporaneous X-ray and optical data were also obtained from the Swift XRT and MDM observatory, respectively. The broadband spectral energy distribution (SED) is well described by a one-zone synchrotron self-Compton (SSC) model favoring a redshift of less than 0.1. Using the photon index measured with Fermi in combination with recent extragalactic background light (EBL) absorption models it can be concluded from the VERITAS data that the redshift of PKS 1424+240 is less than 0.66. Show Partial Abstract