  We present the first case of strong gravitational lensing by a QSO : SDSS
J0013+1523, at z = 0.120. The discovery is the result of a systematic search
for emission lines redshifted behind QSOs, among 22298 spectra of the SDSS data
release 7. Apart from the z = 0.120 spectral features of the foreground QSO,
the spectrum of SDSS J0013+1523 also displays the OII and Hbeta emission lines
and the OIII doublet, all at the same redshift, z = 0.640. Using sharp Keck
adaptive optics K-band images obtained using laser guide stars, we unveil two
objects within a radius of 2 arcsec from the QSO. Deep Keck optical
spectroscopy clearly confirms one of these objects at z = 0.640 and shows
traces of the OIII, emission line of the second object, also at z = 0.640. Lens
modeling suggests that they represent two images of the same z = 0.640
emission-line galaxy. Our Keck spectra also allow us to measure the redshift of
an intervening galaxy at z = 0.394, located 3.2 arcsec away from the line of
sight to the QSO. If the z = 0.120 QSO host galaxy is modeled as a singular
isothermal sphere, its mass within the Einstein radius is M_E(r < 1 kpc) =
2.16e10 M_Sun and its velocity dispersion is sigma_SIS = 169 km/s. This is
about 1 sigma away from the velocity dispersion estimated from the width of the
QSO Hbeta emission line, sigma_*(M_BH) = 124 +/- 47 km/s. Deep optical HST
imaging will be necessary to constrain the total radial mass profile of the QSO
host galaxy using the detailed shape of the lensed source. This first case of a
QSO acting as a strong lens on a more distant object opens new directions in
the study of QSO host galaxies.
