As is often the case with Sonic games, not always mind, you can find a Chaos Emerald in a bonus stage. In these stages you have to grapple onto balls floating in the ether and swing your way closer to the emerald, you can collect rings to increase the timer and there are boost spots you can swing into to get you closer faster. It takes some getting used to.
Once you reach the emerald make sure to lock on and grab it, this will give you a new power called Avatar which you can used to smash through blocks by first selecting it with the right stick and pressing X.