Chip is one of Mrs. Potts' apparently numerous children and the only one who we really meet. Aside from the fact that he's a living tea cup, he's pretty much your standard-issue kid. He's earnest, enthusiastic, and friendly, with a lot of curiosity and the slightest bit of mischief thrown into his DNA. He's the first one to announce Belle's arrival with a "Mama! There's a girl in the castle!" When she leaves, he stows away in her satchel…allowing him to come to the rescue when Gaston and the mob lock Belle and Maurice in the cellar.
Frankly speaking, that's why he's here—we already have three other servants to act as comic relief. But, he also makes a nice surrogate for any little kids in the audience, and his devotion to Belle is self-evident by his absolute unwillingness to let her leave without tagging along. "Why did you go away? Don't you like us anymore?" he asks her plainly, showing us exactly how much he's come to care about her.
Basically, he's a peppy little advance scout for the rest of the serving staff: always ready to help with a smile and a way of staying cheerful.