... It means that it wants to be fed and mothered. Clyde would sometimes make this noise when someone came up to the cage too. He would squeak at a family member when they came to see him.
Feel very honored ... Clyde was telling you not only did he want to be a part of your family, but he considers you a "big chin" and a part of his family ... a very, very big compliment from a chinchilla. He's showing he loves you and wants to stay with you.

Give him a sniff and a chinnie kiss for me.

A chinnie sniff is when a chinchilla greets another chin ... they sniff each other's noses and usually down the side a little ways ... this is the 'proper'/'polite' greeting between chinchillas.

Jo Ann