  The brightest cluster galaxy (BCG) in the Abell 1664 cluster is unusually
blue and is forming stars at a rate of ~ 23 M_{\sun} yr^{-1}. The BCG is
located within 5 kpc of the X-ray peak, where the cooling time of 3.5x10^8 yr
and entropy of 10.4 keV cm^2 are consistent with other star-forming BCGs in
cooling flow clusters. The center of A1664 has an elongated, "bar-like" X-ray
structure whose mass is comparable to the mass of molecular hydrogen, ~ 10^{10}
M_{\sun} in the BCG. We show that this gas is unlikely to have been stripped
from interloping galaxies. The cooling rate in this region is roughly
consistent with the star formation rate, suggesting that the hot gas is
condensing onto the BCG. We use the scaling relations of Birzan et al. 2008 to
show that the AGN is underpowered compared to the central X-ray cooling
luminosity by roughly a factor of three. We suggest that A1664 is experiencing
rapid cooling and star formation during a low-state of an AGN feedback cycle
that regulates the rates of cooling and star formation. Modeling the emission
as a single temperature plasma, we find that the metallicity peaks 100 kpc from
the X-ray center, resulting in a central metallicity dip. However, a
multi-temperature cooling flow model improves the fit to the X-ray emission and
is able to recover the expected, centrally-peaked metallicity profile.
