Sounds like a void in the casting that was covered over with the chrome or enamel finish, that finally gave way. I would see if manufacturer will replace for free as a manufacturing defect. If a tiny pinhole, draining the water out and then drying with a hair dryer and shoving some epoxy putty in might seal it - no telling how long that would last, though.
You do not have to replace the sink if only the faucet is holed - or did you mean the sink has a hole. Faucet can be pulled out and replaced with a comparable one that is designed to fit in same size hole(s) - typically about $50-100 for the fuacet unless you get pretty fancy,, and about $100-150 should handle the install.
If small sink hole (pinhole, not finger sized), plumber might be able to fix with some epoxy patch putty, then sand and touch up with matching paint. Likely about $150 repair cost.