A seal arc segment includes a wall that defines radially inner and outer sides, forward and aft ends, and first and second circumferential sides. The wall includes a CMC ply lay-up of a radially inner-most CMC ply on the inner side, a radially outer-most CMC ply on the radially outer side, and radially intermediate CMC plies therebetween. At least one of the radially intermediate CMC plies has cutout voids that define cooling channels in the wall. The cooling channels are bound on lateral channel sides by the at least one of the radially intermediate CMC plies, bound on a radially inner channel side by a first adjacent one of the CMC plies, and bound on a radially outer channel side by a second, different adjacent one of the CMC plies. The radially outer-most CMC ply includes at least one inlet hole connected to the cooling channels for providing cooling air.