Former U.S. President Bill Clinton says raising his daughter, Chelsea, was the most important job he and his wife, Secretary of State Hillary Clinton, ever had.

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Bill Clinton made the remarks about his adult daughter on Monday's edition of "Late Show with David Letterman" on CBS.

"Tremendous responsibility being a parent -- being a parent and having people at the highest profile of public figures and awareness, that must be nearly impossible. Everybody points to what a great job you and your wife did with your daughter. How do you keep that in proper perspective, proper balance?" Letterman asked Clinton.

"I give a lot of credit to her mother and I give a lot of credit to her, but we worked at it," Clinton replied. We always tried to make her feel special and that she was loved, but not special because of who her parents were. And I think she lives that way. And, you know, I don't think there's -- it's not really mysterious ... Kids keep score, they pay attention, and you need to be there for them. And they know if you have to work, they get that, but I think that -- you know, there was a study about, oh, 15, 20 years ago about people who made it against all the odds. Every one of them had a caring adult in their lives who made them feel like they were the most important person in the world to them. I don't think this is really rocket science, but I do give a lot of credit to my daughter and to her mother, but we worked at it. And we only were able to have one child, and we really always thought it was our most important job, Hillary and I both did."