  The ubiquity of Lyman alpha (Ly$\alpha$) emission in a sample of four bright
[O III]-strong star-forming galaxies with redshifts above 7 has led to the
suggestion that such luminous sources represent a distinct population compared
to their fainter, more numerous, counterparts. The presence of Ly$\alpha$
emission within the reionization era could indicate that these sources created
early ionized bubbles due to their unusually strong radiation, possibly due to
the presence of active galactic nuclei. To test this hypothesis we have secured
long integration spectra with XSHOOTER on the VLT for three $z\simeq$7 sources
selected to have similar luminosities and prominent excess fluxes in the IRAC
3.6 or 4.5$\mu$m band, usually attributed to strong [O III] emission. We
secured additional spectroscopy for one of these galaxies at $z$=7.15 using
MOSFIRE at the Keck telescope. For this, the most well-studied source in our
sample with the strongest IRAC excess, we detect prominent nebular emission
from He II and NV indicative of a non-thermal source. For the other two sources
at $z$=6.81 and $z$=6.85, for which no previous optical/near infrared
spectroscopy was initially available, Ly$\alpha$ is seen in one and CIII]
emission in the other. Although a modest sample, our results further support
the hypothesis that the phenomenon of intense [O III] emission is associated
preferentially with sources lying in early ionized bubbles. However, even
though one of our sources at $z$=7.15 clearly indicates the presence of
non-thermal radiation, such ionized bubbles may not uniquely arise in this
manner. We discuss the unique advantages of extending such challenging
diagnostic studies with JWST.
