In my short own short experience with chinchillas I've witnessed them do some pretty stupid things. I think they can see well enough but I don't think they can always read the environment in terms of slipperiness, movement, or stability, which makes sense because growing up they don't experience much outside of their cage. In the wild I image they would be impressively agile.
Just a couple of days ago my chinchilla jumped out of my hands as I returned him to his cage. He didn't want to go back so he jumped towards me unexpectedly and hit his head on the edge of the cage frame and flopped onto the floor. He was in shock and I was able to pick him up. (Usually he runs off when he gets out.) It was very worrisome for a while. I gave him some white paper to chew on so I could check for signs of blood but didn't find any. He seems to be fine today. It wouldn't be the first time he tried to get out like that but that was the first time he had such a hard landing and I pray his teeth are okay.
With that being said I let my three month old chinchilla ride on my shoulder without any problems. (who is now 6 months) He doesn't try to jump off unless he thinks there's something he can land on such as my arm. If he misses I can catch him easily before he hits the floor. One time he did get down when he jumped on my arm when I was holding a cup of coffee and then he slipped off and I couldn't catch him. (I use instant coffee and don't heat the water hot enough to cause burns, btw.) I was able to catch him after I put the cup down and corner him in an adjacent room. I would just say don't stand next to anything that would be hazardous to fall onto. Eventually it will happen and you'll never know exactly how it will play out. I don't think your chinchilla will jump off without warning under normal circumstances. If it does I don't think it will get hurt unless it falls onto something that is hard. However freak accidents can happen so be careful.