You don't need chains for 3* (or 4* for that matter). I sub 30'd all the 3* without ever using chains and I'm pretty shit (still haven't beaten all the 4*).

Rather than focus on a specific comp that you can't achieve, just pick the element you think you're the best at, even if you have a sub-par USB it can still be useful, I used Paine with her USB and Yuffie with her BSB1 as DPS for my first magicite clear.

Just pick your best element, with your best healer, and your best support. You may even want to consider two healers depending on your DPS.

It took me probably more than a dozen tries to beat my first 3 star magicite, but once you can beat one, you can start farming it for more magicite, and even just 3 star magicite can make a HUGE difference when they're leveled up.