Recent years have seen a surge in work on Person Hierarchy Effects (Béjar and Rezac 2009; Georgi 2011; Lochbihler 2009; Nevins 2007, 2011; Oxford 2014; Walkow 2009; Wiltschko 2008). In this paper, I analyze a curious case of such an effect which has been widely discussed in theoretical and descriptive work on the Quechua family (van de Kerke 1996; Lakämper and Wunderlich 1998; Milliken 1984; Muysken 1981; Weber 1976, 1989). In many Quechua languages, objects bearing the feature [Addressee] interact with subject agreement, but 1st person exclusive objects do not, even in the presence of a 3rd person subject. I dub this effect the [Addressee]-driven Subject Marking Anomaly (A-SMA), adapting the terminology of Weber (1976). After showing that object markers in Quechua languages are in fact object clitics, I argue that the A-SMA emerges from the interaction of cliticization with subject agreement: [Addressee] clitics raise above the subject in the clausal hierarchy, thus feeding agreement, but non-[Addressee] clitics do not. The analysis is extended to a related agreement effect involving plural objects in certain Bolivian and Argentine varieties of Quechua.