The story
The first dramatic play presented in the Romanian language (and one of the first theatrical performance in Romanian) was Mirtil and Hloe, adapted and staged by Gheorghe Asachi, and held in the capital (Jassy/Iași) of Moldavia, on 27 December 1816. In 1834, a Romanian production took place in Iași on the stage of the Théâtre de varieté, built in 1832 for the French Fouraux troupe.
The National Theatre was founded on 15 May 1840, as the Great Theatre of Moldavia, when the Romanian language troupe, led by Costache Caragiali, was united with the French troupe, under a single direction of Vasile Alecsandri and the management of Costache Caragiali. On 22 December 1846, a new audience hall was inaugurated in the former mansion of Prince Mihail Sturdza, on the Hill of Copou.
From Wikipedia’s article on Iași National Theatre, shared under CC BY-SA 4.0.4

