@piyush, thank you for asking. Accepting partial payments is currently not available but it is in our pipeline.
As a workaround you can add comments to the pending invoice and enter how much you've received so far. Once you've received the remaining amount, you can record the payment in the invoice and ChargeBee will close it automatically.
Partial is a must - even Magento and shopping carts allows it as generic feature. Many big companies establish long contract - where partial invoice payments are set and paid month by month to fulfill the contract