One of the things that I do with my chinchillas and encourage people who buy chinchillas from me to do is to sit with my hands facing palms up by the cage door. I let the chinchillas come to me and crawl onto my hands. It takes time and they will generally get very nervous and jump right back in the cage after climbing onto my palms, but (with time and patience) they will start to jump onto my hands and will allow me to move my hands and arms so that I can transport them for play time. I try to use this method instead of chasing them around the cage and grabbing them, since this frightens them and makes them associate me with something negative.
Yesterday, in fact, I had some people over to see the chinchillas. I had one of the cage doors open to try to encourage some of the chins to come out and one of my boys who is normally VERY shy determined that he wasn't so shy anymore! Anytime one of us put our hands up to the cage, he would jump right out onto them, ready to play!