  Bismuth oxyselenide (Bi$_2$O$_2$Se) attracts great interest as a potential
n-type complement to p-type thermoelectric oxides in practical applications.
Previous investigations were generally focused on polycrystals. Here, we
performed a study on the thermoelectric properties of Bi$_2$O$_2$Se single
crystals. Our samples exhibit electron mobility as high as 250
cm$^2.$V$^{-1}$.s$^{-1}$ and thermal conductivity as low as $2$
W.m$^{-1}$.K$^{-1}$ near room temperature. The maximized figure of merit is
yielded to be 0.188 at 390 K, higher than that of polycrystals. Consequently, a
rough estimation of the phonon mean free path ($\ell_\textrm{ph}$) from the
kinetic model amounts to 12 $\r{A}$ at 390 K and follows a $T^{-1}$ behavior.
An extrapolation of $\ell_\textrm{ph}$ to higher temperatures indicates that
this system approaches the Ioffe-Regel limit at about 1100 K. In light of the
phonon dispersions, we argue that the ultralow $\ell_\textrm{ph}$ is attributed
to intense anharmonic phonon-phonon scattering, including Umklapp process and
acoustic to optical phonon scattering. Our results suggest that single crystals
provide a further improvement of thermoelectric performance of Bi$_2$O$_2$Se.
