In this context I would say, "we should divide the chairs among us". Distribute would be often used in a context where you have a set number of chairs, but an undefined number of people. Someone else may have a better answer than this :)

Divide works. Distribute is used more when you handing something out yourself (e.g. you have £100 and are giving £10 out to ten different people) but it would still be understood I think. Share and Split are both common when it's something you are doing within a group such as "We should split the work." or "We should share the chairs between us.". Split usually implies the share is going to be equal.