C.V.
He's fine. I used to take naps on the couch with my baby sleeping on my chest (on his tummy).
I know I'm going to get blasted for this, but even if he slept on his tummy ALL the time, it's very unlikely anything would happen. SIDS is very rare. It was rare even when most babies were put to sleep on their tummies.
SIDS isn't CAUSED by babies sleeping on their tummies. Even though the back-to-sleep campaign has reduced SIDS mortality rates over the last 30 years by about half, babies still die of SIDS each year. Which means that tummy sleeping isn't the primary cause. There's still another reason thousands of babies die from SIDS each year. Many researchers believe that those babies' brains simply weren't developed fully to be able to maintain breathing during sleep (sleep apnea), but that's just another theory.
Soooooo...I say none of that to scare you. I say it because I want you to know that it's okay to allow your baby to tummy sleep in your presence, and when he's 6 months (or rolling back and forth reliably), he can sleep however he likes. He'll be just fine.