Christensen (p. 204, n. 512): "Aj Tz'ikina Ja (They of the Bird House) was the dominant lineage of the people today known as the Tzutuhils [Tz'utujil], who occupied the land from the southern shores of Lake Atitlán south to the cacao-growing land of the Pacific Coast. Their capital was Chiya' (now called Chutinamit), located on a small hill at the base of San Pedro Volcano just across the bay to the northwest of the modern community of Santiago Atitlán. The group was likely composed of two separate lineage groups (the Ah Tziquinahas and the Tzutuhils), which were at times openly hostiel to one another (Orellana 1984, 81; Carlsen 1997, 75). The authors of the Annals of the Cakchiquels stated that the Tzutuhils succeeded in temporarily expelling the Ah Tziquinahas from their citadel south of Lake Atitlán in 1521 (Recinos and Goetz 1952, 117)."
Carlsen (2001, pp. 284–285) adds: "Tz'utujil, which means 'flower of the maize plant,' is a language of the Greater K'iche'an (or K'iche'an-Mamean branch of the Eastern division of the Mayan language family." "Until the subsequent arrival of the Kaqchikel, the entire Lake Atitlán region, as well as extensive areas in the agriculturally rich piedmont region, was under Tz'utujil control. The exact nature of that control remains a point of scholarly debate. Sandra Orellana argues for a single Tz'utujil kingdom; in contrast, I propose the coexistence of competing Tz'utujil polities [one of which, presumably, would be the Ajtz'ikinajas].""When the Spanish arrived in 1524, much of the former Tz'utujil territory had been seized by the more numerous Kaqchikel. Led by Pedro de Alvarado, the Spanish force exploited preexisting regional hostility and enlisted the Kaqchikels as allies to defeat the Tz'utujils."
The prefix aj- refers to a person associated with a place, object, or activity, tz'ikin means "bird," and ja refers to "house." Thus this name can be translated as "those of the bird house."