  The Extragalactic Background Light (EBL) captures the total integrated
emission from stars and galaxies throughout the cosmic history. The amplitude
of the near-infrared EBL from space absolute photometry observations has been
controversial and depends strongly on the modeling and subtraction of the
Zodiacal light foreground. We report the first measurement of the diffuse
background spectrum at 0.8-1.7 um from the CIBER experiment. The observations
were obtained with an absolute spectrometer over two flights in multiple sky
fields to enable the subtraction of Zodiacal light, stars, terrestrial
emission, and diffuse Galactic light. After subtracting foregrounds and
accounting for systematic errors, we find the nominal EBL brightness, assuming
the Kelsall Zodiacal light model, is 42.7+11.9/-10.6 nW/m2/sr at 1.4 um. We
also analyzed the data using the Wright Zodiacal light model, which results in
a worse statistical fit to the data and an unphysical EBL, falling below the
known background light from galaxies at <1.3 um. Using a model-independent
analysis based on the minimum EBL brightness, we find an EBL brightness of
28.7+5.1/-3.3 nW/m2/sr at 1.4 um. While the derived EBL amplitude strongly
depends on the Zodiacal light model, we find that we cannot fit the spectral
data to Zodiacal light, Galactic emission, and EBL from solely integrated
galactic light from galaxy counts. The results require a new diffuse component,
such as an additional foreground or an excess EBL with a redder spectrum than
that of Zodiacal light.
