We present the mid-infrared star formation rates of 245 X-ray selected, nearby (z<0.1) brightest cluster galaxies (BCGs). A homogeneous and volume limited sample of BCGs was created by X-ray selecting clusters with Lx>1x10^44^erg/s. The Wide-Field Infrared Survey Explorer (WISE) All WISE Data Release provides the first measurement of the 12{mu}m star formation indicator for all BCGs in the nearby Universe. Perseus A and Cygnus A are the only galaxies in our sample to have star formation rates of >40M_{sun}_/yr, indicating that these two galaxies are highly unusual at current times. Stellar populations of 99+/-0.6 per cent of local BCGs are (approximately) passively evolving, with star formation rates of <10M_{sun}_/yr. We find that in general, star formation produces only modest BCG growth at the current epoch.