Chipped the back part of my left front tooth - sensitive to coldness, what will the dentist do?

So the tooth is now sensitive to cold drinks in my mouth, there's no pain at all otherwise. Brushing that tooth does not hurt. The chip in comparison to the size of the whole tooth isn't that big, but it's still a concern, I can feel it when ever my tongue licks it. Would they just give me a filling as in like a cavity, or would they go as far as to trim the tooth down ( remember the chip isn't even that big in comparison to the size of the whole tooth ) and put a cap over it?