A basic first aid kit should include the following:

• EMERGENCY VET CONTACT DETAILS 
• STERILE DROPPERS OR SYRINGES  - for administering oral meds, eye washes and for hand feeding. 
• CRITICAL CARE - a nourishment product for chins that are not eating.
• ANTI FUNGAL POWDER - used in dust baths as a preventitive for ringworm, also works as a cure.
• CORN STARCH - helps stop bleeding.
• ANTIBIOTIC CREAM - for wounds. Wounds must be cleaned first to prevent trapping infection.
• PEDIALYTE - to replace fluids.
• INFACOL - to help with bloat. Chinchillas don't fart or burp and can be prone to bloat.
• SALINE - to clean wounds and flush eyes
• TOWELS - for wrapping chin to administer meds.
• SMALL PAIR OF SCISSORS 
• COTTON SWABS OR COTTON BUDS - to apply topical meds
• STERILE PADS
• GAUZE WRAP OR VET WRAP
• UNSCENTED BABY WIPES - to clean soiled fur
• CARRY CASE - to transport chin to vet
• 1% HYDROCORTISONE CREAM - to relieve itching and irritation.
• PEN AND NOTE PAD.
• URINE DIP TEST STRIPS - used to test urine for UTI's, using 10 parameters strips will show the ph level and if blood and protein are present, the natural ph level of chinchilla urine is 8-9.

Even if your chin is healthy it's good to keep a note of their weight every 2 weeks. A drop of more than 20g should be investigated by an exotic vet.

Hopefully you won't have any need to use your first I'd kit. Keep an eye on use by dates, discarding any past their date.