Hey James,
I had a similar issue a few months back when I had a bunch of chases on subs and wanted them in my cue stack at various points during the show, I found a bit of a work around that might work for you to.
If you change the trigger of the sub with the chase to 'latch' (I think its latch im not at my board right now) the sub will run the chase when its flash button is pressed and end it when pressed again. You can then create a macro that presses that flash button for you (and so start and stop your chase) this macro can then be fired from a cue.
Hope this helps, like I say it worked for my show and was particularly helpful when I wanted to have two chases running at once and then take one of the chases away while keeping the other running, got a little confusing at times while I was programming but it worked a treat come the show.
Hope this helps,
John.