We have found that the brightest cluster galaxy (BCG) in A85, Holm 15A, displays the largest core known so far. Its cusp radius, r sub(gamma) = 4.57 + or - 0.06 kpc (4."26 + or - 0."06), is more than 18 times larger than the mean for BCGs and > ~ 1 kpc larger than A2261-BCG, hitherto the largest-cored BCG. Holm 15A hosts the luminous amorphous radio source 0039-095B and has the optical signature of a LINER. Scaling laws indicate that this core could host a supermassive black hole (SMBH) of mass M sub(bullet) ~ (10 super(9)-10 super(11)) M sub(middot in circle). We suggest that cores this large represent a relatively short phase in the evolution of BCGs, whereas the masses of their associated SBMH might be set by initial conditions.