  We present new Chandra X-ray Observatory and Hubble Space Telescope
observations of eight optically selected broad-line AGN candidates in nearby
dwarf galaxies ($z<0.055$). Including archival Chandra observations of three
additional sources, our sample contains all ten galaxies from Reines et al.
(2013) with both broad H$\alpha$ emission and narrow-line AGN ratios (6 AGNs, 4
Composites), as well as one low-metallicity dwarf galaxy with broad H$\alpha$
and narrow-line ratios characteristic of star formation. All eleven galaxies
are detected in X-rays. Nuclear X-ray luminosities range from $L_{0.5-7
\rm{keV}}\approx5\times10^{39}$ to $1\times10^{42}$ $\rm{erg}\rm{s^{-1}}$. In
all cases except for the star forming galaxy, the nuclear X-ray luminosities
are significantly higher than would be expected from X-ray binaries, providing
strong confirmation that AGN and composite dwarf galaxies do indeed host
actively accreting BHs. Using our estimated BH masses (which range from
$\sim7\times10^{4}-1\times10^{6}~M_{\odot}$), we find inferred Eddington
fractions ranging from $\sim0.1-50\%$, i.e. comparable to massive broad-line
quasars at higher redshift. We use the HST imaging to determine the ratio of
ultraviolet to X-ray emission for these AGN, finding that they appear to be
less X-ray luminous with respect to their UV emission than more massive quasars
(i.e. $\alpha_{\rm OX}$ values an average of 0.36 lower than expected based on
the relation between $\alpha_{\rm OX}$ and $2500{\rm \AA}$ luminosity).
Finally, we discuss our results in the context of different accretion models
onto nuclear BHs.
