  The first measurement of dielectron ($\mathrm{e}^{+}\mathrm{e}^{-}$)
production in central (0$-$10$\%$) Pb-Pb collisions at
$\mathbf{\sqrt{{\textit{s}}_{\mathrm{NN}}}}$ = 2.76 TeV at the LHC is
presented. The dielectron invariant-mass spectrum is compared to the expected
contributions from hadron decays in the invariant-mass range $0 <
m_{\mathrm{ee}}<3.5\ \mathrm{GeV}/\textit{c}^{2}$. The ratio of data and the
cocktail of hadronic contributions without vacuum $\rho^{0}$ is measured in the
invariant-mass range $0.15 < m_{\mathrm{ee}}<0.7\ \mathrm{GeV}/\textit{c}^{2}$,
where an excess of dielectrons is observed in other experiments, and its value
is $1.40 \pm 0.28\ (\mathrm{stat.}) \pm 0.08\ (\mathrm{syst.}) \pm 0.27\
(\mathrm{cocktail})$. The dielectron spectrum measured in the invariant mass
range $0 < m_{\mathrm{ee}}<1\ \mathrm{GeV}/\textit{c}^{2}$ is consistent with
the predictions from two theoretical model calculations that include thermal
dielectron production from both partonic and hadronic phases with in-medium
broadened $\rho^{0}$ meson. The fraction of direct virtual photons over
inclusive virtual photons is extracted for dielectron pairs with invariant mass
$0.1 < m_{\mathrm{ee}}<0.3\ \mathrm{GeV}/\textit{c}^{2}$, and in the
transverse-momentum intervals $1<p_{\mathrm{T}, \mathrm{ee}}<2\
\mathrm{GeV}/\textit{c}$ and $2<p_{\mathrm{T}, \mathrm{ee}}<4\
\mathrm{GeV}/\textit{c}$. The measured fraction of virtual direct photons is
consistent with the measurement of real direct photons by ALICE and with the
expectations from previous dielectron measurements at RHIC within the
experimental uncertainties.
