  We present the results of GALEX observations of 17 cool core (CC) clusters of
galaxies. We show that GALEX is easily capable of detecting star formation in
brightest cluster galaxies (BCGs) out to $z\ge 0.45$ and 50-100 kpc. In most of
the CC clusters studied, we find significant UV luminosity excesses and colors
that strongly suggest recent and/or current star formation. The BCGs are found
to have blue UV colors in the center that become increasingly redder with
radius, indicating that the UV signature of star formation is most easily
detected in the central regions. Our findings show good agreement between UV
star formation rates and estimates based on H$\alpha$ observations. IR
observations coupled with our data indicate moderate-to-high dust attenuation.
Comparisons between our UV results and the X-ray properties of our sample
suggest clear correlations between UV excess, cluster entropy, and central
cooling time, confirming that the star formation is directly and
incontrovertibly related to the cooling gas.
