Ultra-wideband 3D imaging spectrometry in the millimeter-submillimeter (mm-submm) band is an essential tool for uncovering the dust-enshrouded portion of the cosmic history of star formation and galaxy evolution. However, it is challenging to scale up conventional coherent heterodyne receivers or free-space diffraction techniques to sufficient bandwidths ($geq$1 octave) and numbers of spatial pixels (>$10^2$). Here we present the design and first astronomical spectra of an intrinsically scalable, integrated superconducting spectrometer, which covers 332-377 GHz with a spectral resolution of $F/Delta F sim 380$. It combines the multiplexing advantage of microwave kinetic inductance detectors (MKIDs) with planar superconducting filters for dispersing the signal in a single, small superconducting integrated circuit. We demonstrate the two key applications for an instrument of this type: as an efficient redshift machine, and as a fast multi-line spectral mapper of extended areas. The line detection sensitivity is in excellent agreement with the instrument design and laboratory performance, reaching the atmospheric foreground photon noise limit on sky. The design can be scaled to bandwidths in excess of an octave, spectral resolution up to a few thousand and frequencies up to $sim$1.1 THz. The miniature chip footprint of a few $mathrm{cm^2}$ allows for compact multi-pixel spectral imagers, which would enable spectroscopic direct imaging and large volume spectroscopic surveys that are several orders of magnitude faster than what is currently possible.
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