Yes, but only in very small amounts.
The reason being is that currants are very high in calcium and acidic content and this is difficult for chinchillas to digest. It may also cause digestion problems for them as their stomachs are highly sensitive.
Only offer them small amounts and not often as it could result in diarrhea and an upset stomach for your chin.
As part of their main diet you should avoid feeding currants to chinchillas as this fruit isn’t ideal for their diet.