  We report the discovery of a Broad Absorption Line (BAL) of \sim 10^4 km s-1
in width in the previously known BL Lac object PKS 0138-097, which we
tentatively identified as a Mg II BAL. This is the first detection of a BAL,
which is sometimes seen in powerful quasars with high accretion rates, in a BL
Lac object. The BAL was clearly detected in its spectra of two epochs at a high
luminosity state taken in the Sloan Digital Sky Survey (SDSS), while it
disappeared in three SDSS spectra taken at a low luminosity state. The BAL and
its variability pattern was also found in its historical multi-epoch spectra in
the literature, but has been overlooked previously. In its high resolution
radio maps, PKS 0138-097 shows a core plus an one-sided parsec-scale jet. The
BAL variability can be interpreted as follows: The optical emission is
dominated by the core in a high state and by the jet in a low state, and the
BAL material is located between the core and jet so that the BAL appears only
when the core is shining. Our discovery suggests that outflows may also be
produced in active galactic nuclei at a low accreting state.
