My first question would be, how old is the chimney?
Reason I ask this is that boring holes in a brick chimney could weaken the structure of the chimney itself.
I have to agree with the comment of ghost about the cable being un-supported on a vertical run, you can't merely have a cable hanging in mid-air.
Regardless of age is there really a concern with structural integrity if there is a 1/2" hole drilled into it? To clarify other comments/suggestions the 4" duct going up the chimney is in a space that is about 8"wide. The BX is only loose in the chimney for about 24" and the rest is straped. If the home owner ever wanted a wood burning fireplace again I guess he would have to remove the BX and fix the holes and liners he drilled trough. Remember I did ask my local inspector if it was acceptable and he had no issues with it.
Personally I don't like it but thats what the customer wanted and it was accepted by inspection.
