If you want you chin to be tame and trusting, you should practice all the steps leading from cage bar tameness to complete tameness very slowly. Daily free run should take place after the chinnie get use to your hand and body so no chase necessary while you want to put your pet back to its cage. You actually will frighten your chins when you are chasing them, and most important, you will lost their trust!
When the first time your chin came to your house, don't let them run free. Since the chin is still not familiar with you, you will only left with the chasing method to get your chin back to the cage. Instead, open the cage door and let this curious little creature to enter its new home and explore the new surrounding.
Since chinchillas are curious animals that react at anytime to everything going on around them, in the first few days, during the daytime, ignore your pet and pretend that the chin doesn't even exit. While at dusk and night, do something around its cage so the chin will approach to the cage bars curiously. And you can start to give out some pellets or treats through the cage bar to begin your taming practice at night. Soon, the little creature will notice that there are no interesting things happen in the daytime and so they will learn their nature bedtime. Their nature naptime is at the daytime and being active at dusk and night. DO NOT TRY TO CHANGE THEIR NATURE BEDTIME!! Any daytime activity will not give them enough sleep during the daytime, and they will not sleep at night, EVER. Enough sleeping is a very good practice for chins' health.
In the process of taming or getting trust from your chin, the first thing is to give out treats or pellets with your hand when they are approaching to the cage bar curiously. Most of the chins are willing to get their pellets or treats from your fingers. Then the next step is to put the treats or pellets on your palm, and wait for your chin to put its front paw on your hand to get its treat. This step is also take place inside the cage so make sure your chin will not jump out so you would not need to catch the chin back to the cage. CHASING YOUR CHIN WILL ONLY INCREASE FRIGHT AND MISTRUST. While they are eating the treats, you can try to scratch their neck carefully. Chins just love it. You can also scratch your chin while they are sleeping at the daytime, and you will find out that they are enjoying it by closing their eyes! They will know that your big hands are not an enemy and sooner or later, they will get used to your hands. If this works, you can then put the treats onto you forearm and wait for the chin to climb up this "new branch" to get the treats. All these step must proceed slowly. Give your chin time to overcome its timidity. It may take up to 6 months to gain trust from your chin, but it really depends on your chin.
If all of the above works, you can start to get your chin to sit on your arm against your body. It really takes time to have things work out. Keep in mind that most of the chin do not like to be handle much because they are so energetic and curious that cannot stay in the same spot in more than a couple seconds. When they are moving around and extending their leg when you are handling them, it doesn't mean that they are afraid of you, they are just cannot wait to explore and run around when they are outside the cage.
I am not sure what is the best way to handle chinnie, but I used to handle my chins by putting one of my hand under the chin to support it and the other hand can just drop down or put on the back of the chin. This method did not apply for all of our chins. Some chins like to be handle in this way, some like to be handle in that way. It depends on the chins. The first attempt may not be success, but by the time it knows it can have a treat as a reward of letting us handle, it will just patiently sit on your hand close to your body and wait for the treat. Remember never catch your chin by pulling their tail and fur, they have the ability to break their tail and furs off when they want to escape from enemies. Never heard of that before, but it is possible because they used to do this in the wild, and their native habitat may not be changed.
Keep in mind that free run only happen after they are not afraid of you anymore. You do not need to "catch" the animal back to its cage. By the time they know they will have a treat for going back to their cage nicely, you will not need to catch them. Our chins did memorized that they can have treat when they get back to the cage. When we open a bag of treat (they did memorized the sound; that's the sound we had made every time we offer them a treat), all of them suddendly rash back to their cages and stand in front of the cage bar waiting for their treats. THAT'S THEIR ROUTINE! Which means you need to do it every time so they will have them memorized, usually withing a week. They are smarter than you think.