  We present the results of a reverberation mapping (RM) campaign on the black
hole (BH) associated with the active galactic nucleus (AGN) in SDSS
J114008.71+030711.4 (hereafter GH08). This object is selected from a sample of
19 candidate intermediate mass BHs (M_{BH} < 10^{6} Msun) found by Greene & Ho
2004 in the Sloan Digital Sky Survey (SDSS). We used the Hobby-Eberly Telescope
to obtain 30 spectra over a period of 178 days in an attempt to resolve the
reverberation time lag (tau) between the continuum source and the broad line
region (BLR) in order to determine the radius of the BLR (R_{BLR}) in GH08. We
measure tau to be 2 days with an upper limit of 6 days. We estimate the AGN
luminosity at 5100 Angstroms to be approximately 1.1 x 10^{43} erg s^{-1} after
deconvolution from the host galaxy. The most well calibrated R_{BLR}-L relation
predicts a time lag which is 4 times larger than what we measure. Using the
measured H\beta\ full-width-at-half-maximum of 703 (+/-) 110 km s^{-1} and an
upper limit for R_{BLR} = 6 light days, we find M_{BH} < 5.8 x 10^{5} Msun as
an upper limit to the BH virial mass in GH08, which implies super-Eddington
accretion. Based on our measured M_{BH} we propose that GH08 may be another
candidate to add to the very short list of AGNs with M_{BH} < 10^{6} Msun
determined using RM.
