You discover that an h.r department employee is discussing confidential information with employees outside the department. How would you handle it?

This becomes a problem especially when HR does NOT respect employee confidentiality. I would go to HR's supervisor or manager and mention this issue. Possibly confront HR and make them aware how ungrateful and unprofessional they are. Make them feel bad in a nice way :)

Initially generalization of the need to keep secrets company and alert everyone to the implementation issue either particular employee was trying to sit down with him, and explain that the system in the company's character kind of secrecy must be maintained on the secrets of the company because of its importance and possible exposure to risk so you'll not debate the mysteries of the company among employees until the employee is not culpable.