We have four cats, who are well behaved about most things, but NOT about prey (which is what they believe chicks are). We raised our chicks indoors for several weeks, without restricting cat access, by making sure our brooders were secure against cat invasion.
Our first brooder was a rubbermaid container with hardware cloth fastened to a 2x4 frame to fit the top. As they got bigger, we moved them to a 2 ft by 6 ft cardboard box, which we lined with a few layers of old towels on the bottom and lots of shavings. For this, we just fastened the hardware cloth top on with wires through holes we made in the cardboard sides. We stress tested it (before putting the chicks in) by putting our largest cat on top. It worked fine, and we found the cats really didn't like the feeling of the hardware cloth under their feet, especially the cardboard box brooder (the hardware cloth moved a bit more, and the cats didn't like the instability, and would jump off).
We let the cats watch the chicks through the hardware cloth top - they were quite entertained. And naturally, the cats would be completely evicted from the room whenever the brooder top was off, either for playing with the chicks or cleaning.