Can a Language Have No Pronouns at All?

Maria had some strange consonant harmonies right in the beginning, like between one and two. Diaper became biper, so the D assimilated to the place of the P and became a B. And catch became chatch with a similar sort of assimilation going on there. Can a language have no pronouns at all, or no pronouns that denote person? That would be an interesting thing to explore.