Jiajak Jaqeli (Georgian: ჯიაჯაყ ჯაყელი) was the Empress consort of Alexios II of Trebizond.
Jiajak was a daughter of Beka I, the Jaqeli atabeg of Samtskhe. The Jaqelis held the Georgian feudal office of Eristavi, which could be "governor of a region" or an "army-commander", roughly equivalent to the Byzantine strategos and normally translated into English as "duke".
The marriage of Jiajak to Alexios II can be estimated to c. 1300. The Byzantine Emperor Andronikos II Palaiologos had been his guardian and wanted Alexios to marry a daughter of the high court official Nikephoros Choumnos, but, without asking for the permission, the young man instead married jiajak Jaqeli. Andronikos appealed to the Church to annul the marriage but the Patriarch refused to assist him, on the ground that Jiajak was reported to be already pregnant. Alexios' mother Eudokia Palaiologina, who returned to Trebizond on the pretext of inducing her son to dissolve the marriage, advised him to keep his Iberian wife.
The duration of their marriage remains uncertain. Alexios died in 1330 but there is no report when Jiajak died. The Dictionnaire historique et Généalogique des grandes familles de Grèce, d'Albanie et de Constantinople (1983) by Mihail-Dimitri Sturdza considers her to be only the first of two wives. The second one being Jidga, the only daughter of Demetre II of Georgia and his second wife Solghar, a Mongol. Demetre II practiced polygamy and had three known wives at the same time. The existence of this daughter is reported in the "Georgian Chronicles". However, the Chronicle does not mention her being married. However older works such as the Europäische Stammtafeln: Stammtafeln zur Geschichte der Europäischen Staaten (1978) by Detlev Schwennicke do not mention any second marriage for Alexios II. As a result, Sturdza's theory is not universally accepted.