If you do it correctly, you can take chins with you in the car frequently. It's really about making the chins comfortable. That means putting them in a carrier that allows for them to feel safe and not scared. You don't just hold them and take them in the car...that could be disastrous.
There may be times when taking a chin for a car ride could be too stressful, but at those times taking a chin out for playtime may cause the same stress. Very sick chins or chins that are in a new environment could stress out greatly. Also, chins that are very old, very young or chins that are not at all used to being around people can have problems - usually an enclosed carrier with a place to hide will help greatly even with these chins.
If you have have a healthy, normal chinchilla, traveling with it isn't a huge deal. Use your best judgement when it comes to taking chins places and observe their comfort level. Be very careful when it come to new places...and don't take chins outside without them being secured in a carrier.