We present WSRT and VLA radio observations of the neutral hydrogen in the radio galaxy Coma A. We detect extended HI absorption against both radio lobes of Coma A, at distances of about 30 kpc from the centre. Coma A is the first radio galaxy in which HI is seen in absorption at such large distances from the nucleus. The match between the velocities of the neutral hydrogen and those of the extended ionized gas suggests that they are part of the same disk-like structure of at least 60 kpc in diameter. Most likely, this gas disk is partly ionised by the bulk motion of the radio lobes expanding into it. The gas mass of this disk is at least 10^9 Msun. The relatively regular structure of the gas disk suggests that a merger occurred involving at least one large gas-rich galaxy, at least a few times 10^8 yr ago.