We present the design, fabrication, and characterization of a broadband leaky lens antenna for broadband, spectroscopic imaging applications. The antenna is designed for operation in the 300-900 GHz band. We integrate the antenna directly into an Al-NbTiN hybrid microwave kinetic inductance detector (MKID) to measure the beam pattern and absolute coupling efficiency at three frequency bands centered around 350, 650, and 850 GHz, covering the full antenna band. We find an aperture efficiency \eta _{ap} \approx 0.4 over the whole frequency band, limited by lens reflections. We find a good match with simulations for both the patterns and efficiency, demonstrating a 1:3 bandwidth in the submillimeter wavelength range for future on-chip spectrometers.