The star formation mechanisms at work in the early universe remain one of the major unsolved problems of modern astrophysics. Many of the luminous galaxies present during the period of peak star formation (between redshifts 1 and 3) were heavily enshrouded in dust, which makes observing their properties difficult at optical wavelengths. However, many spectral lines exist at far-infrared wavelengths that serve as tracers of star formation during that period, in particular fine structure lines of nitrogen, carbon, and oxygen, as well as the carbon monoxide molecule. Using an observation technique known as intensity mapping, it would be possible to observe the total line intensity for a given redshift range even without detecting individual sources. Here, we describe a detector system suitable for a balloonborne spectroscopic intensity mapping experiment at far-infrared wavelengths. The experiment requires an “integralfield” type spectrograph, with modest spectral resolution (R~100) for each of a number of spatial pixels spanning several octaves in wavelength. The detector system uses lumped-element kinetic inductance detectors (LEKIDs), which have the potential to achieve the high sensitivity, low noise, and high multiplexing factor required for this experiment. We detail the design requirements and considerations, and the fabrication process for a prototype LEKID array of 1600 pixels. The pixel design is driven by the need for high responsivity, which requires a small physical volume for the LEKID inductor. In order to minimize two-level system noise, the resonators include large-area interdigitated capacitors. High quality factor resonances are required for a large frequency multiplexing factor. Detectors were fabricated using both trilayer TiN/Ti/TiN recipes and thin-film Al, and are operated at base temperatures near 250 mK.