  We present new measurements of the large scale clustering component of the
cross-power spectra of the source-subtracted Spitzer-IRAC Cosmic Infrared
Background (CIB) and Chandra-ACIS Cosmic X-ray Background (CXB) surface
brightness fluctuations. Our investigation uses data from the Chandra Deep
Field South (CDFS), Hubble Deep Field North (HDFN), EGS/AEGIS field and
UDS/SXDF surveys, comprising 1160 Spitzer hours and $\sim$ 12 Ms of Chandra
data collected over a total area of 0.3 deg$^2$. We report the first
($>$5$\sigma$) detection of a cross-power signal on large angular scales >20
arcsec between [0.5-2] keV and the 3.6 and 4.5$\mu$m bands, at $\sim$5$\sigma$
and 6.3$\sigma$ significance, respectively. The correlation with harder X-ray
bands is marginally significant. Comparing the new observations with existing
models for the contribution of the known unmasked source population at $z<$7,
we find an excess of about an order of magnitude at 5$\sigma$ confidence. We
discuss possible interpretations for the origin of this excess in terms of the
contribution from accreting early black holes, including both direct collapse
black holes and primordial black holes, as well as from scattering in the
interstellar medium and intra-halo light.
