  We present the first results from the Las Cumbres Observatory Global
Telescope (LCOGT) Network's Active Galactic Nuclei Key Project, a large program
devoted to using the robotic resources of LCOGT to perform time domain studies
of active galaxies. We monitored the Seyfert 1 galaxy Arp~151 (Mrk~40) for
$\sim$200 days with robotic imagers and with the FLOYDS robotic spectrograph at
Faulkes Telescope North. Arp~151 was highly variable during this campaign, with
$V$-band light curve variations of $\sim$0.3 mag and H$\beta$ flux changing by
a factor of $\sim$3. We measure robust time lags between the $V$-band continuum
and the H$\alpha$, H$\beta$ and H$\gamma$ emission lines, with
$\tau_\mathrm{cen} = 13.89^{+1.39}_{-1.41}$, 7.52$^{+1.43}_{-1.06}$ and
7.40$^{+1.50}_{-1.32}$ days, respectively. The lag for the \ion{He}{2}
$\lambda4686$ emission line is unresolved. We measure a velocity-resolved lag
for the H$\beta$ line, which is clearly asymmetric with higher lags on the blue
wing of the line which decline to the red, possibly indicative of radial
inflow, and is similar in morphology to past observations of the H$\beta$
transfer function shape. Assuming a virialization factor of $f$=5.5, we
estimate a black hole mass of
$M_\mathrm{BH}=6.2^{+1.4}_{-1.2}\times$10$^{6}$~$M_{\odot}$, also consistent
with past measurements for this object. These results represent the first step
to demonstrate the powerful robotic capabilities of LCOGT for long-term, AGN
time domain campaigns that human intensive programs cannot easily accomplish.
Arp 151 is now one of just a few AGN where the virial product is known to
remain constant against substantial changes in H$\beta$ lag and luminosity.
