I didn't make any reference to using an A/C chase. If it's a chase for
pipes
and wires it's fine, but don't be running Romex inside of any plenums
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So the A/C chase is or isn't legal?

This "plenum" (if it is one? not sure) is pretty dang big. It's
about a 4 x 3 foot area dead zone in each floor. The A/C stuff is in
one corner leaving basically a large coat closet's worth of dead space
on each floor.