This paper inquires into two issues of Hungarian PPs. Firstly, when Hungarian pronouns bear an oblique case, the case marker must be followed by possessive agreement. Secondly, this pronoun-case-agreement order contrasts with the order found in garden variety possessive structures: ordinary possessive DPs feature the order noun-agreement-case. The goal of this paper is to offer an account of these puzzling phenomena. I argue that a PP structure in which PPs are projected from a silent place noun and the Ground is merged as the possessor of place (Terzi 2005, 2008, 2010; Botwinik-Rotem 2008; Botwinik-Rotem and Terzi 2008; Pantcheva 2008; Cinque 2010a; Noonan 2010, and Nchare and Terzi 2014) allows an enlightening analysis of the appearance and position of the possessive agreement in PPs. I also discuss how certain surface differences between PPs and ordinary possessive constructions can be accounted for while maintaining the possessive analysis of PPs. By showing that a PP structure with a possessive core yields a natural account of the intricate Hungarian data, the paper strengthens the case for a possessive-based approach to PPs in Universal Grammar.