The opera opens in the sacred forest of the Druids during the period of the Roman occupation of Gaul in the first century B.C. Oroveso the high priest announces to a gathering of Gallic warriors and priests that Norma, his daughter who is the only priestess able to interpret the oracles of Irminsul their god, will soon arrive to perform the rite of cutting the sacred mistletoe and prophesy the fall of the hateful Romans.
As the Druids disperse, Pollione the Roman Proconsul enters with his friend Flavio. Norma has broken her vows, has been secretly married to Pollione and has borne him two children. Pollione confides to Flavio that he no longer loves Norma but has lost his heart to the young novice Adalgisa. The two Romans flee as Norma arrives with her procession. She imposes peace upon the Gauls, prophesying that Rome will fall through its own vices but not before the Gallic arms. She then leads the celebrated lyric prayer (Casta Diva) for peace to the moon goddess. As the crowd disperses, Adalgisa remains to meet Pollione who implores her to fly with him to Rome.
In her dwelling, Norma explains to her friend Clotilde that, since Pollione left her, she both loves and hates her children. Adalgisa enters and remorsefully confesses her sinful love to her much revered priestess. Norma, recognising her own fate, promises to release Adalgisa from her vows to join her lover. However, when she learns that it is Pollione who is just then approaching, she reviles him as a traitor. The act closes which a violent scene in which Norma is threatening, Pollione defiant, and Adalgisa entreating Norma to pardon her.
In her despair, Norma intend to kill her two sleeping children but cannot carry out the terrible deed. She sends for Adalgisa, tells the novice that she plans to kill herself, and bids Adalgisa to take the children to Pollione and be their mother. Adalgisa, however, will not hear of this and offers to bring Pollione back to Norma who takes courage again and the two swear eternal friendship.
The Gallic warriors assemble outside the temple to discuss plans to rise against the Romans. Norma meanwhile is impatiently awaiting news. Clotilde brings the message that Pollione refuses to return to her. ln a fury Norma calls to her people to take up arms against the Romans. Pollione is captured in the act of carrying off Adalgisa and is to be the first sacrifice. Norma commands her people to leave her alone with the prisoner and promises him his life if he will leave Gaul without Adalgisa. Pollione refuses and pleads only mercy for Adalgisa, while he is ready to die. Norma summons her Druids and announces that she will expose a priestess who, betraying her vows, has entertained a sinful passion and deserves death. She then denounces herself and steps firmly to the funeral pyre, confiding only to her father the secret of her children and commending to his care. Pollione, recognising Norma’s nobility of heart, feels his love revive and stepping forth joins Norma to meet death in the flames.