When Chita Rivera steps solemnly to the edge of the stage in the opening scene of “The Visit,” she sweeps the audience with a gaze that could freeze over hell. Yet a quickening warmth spreads through the Lyceum Theater, where this macabre, long-gestating Kander and Ebb musical opened on Thursday night. The woman who stands so regally before us may appear as glacial as Siberia. But longtime theatergoers know that beneath the frost, this ice queen is hot stuff. Based on Friedrich Dürrenmatt’s fabular 1956 drama of greed and vengeance, “The Visit” arrives with lots of baggage. That includes the ominous black valises that figure prominently in the show’s set and the many obstacles and alterations this musical has experienced on a 13-year-long journey to Broadway. But it’s the history that the 82-year-old Ms. Rivera carries and the expertise with which she deploys it that keep the chill off this elegant dirge of a production, directed by John Doyle. Portraying a woman with a storied past, she brings with her the legacy of more than six decades as a Broadway musical star. That career has had its spectacular peaks (the creation of classic roles in the original “West Side Story” and “Chicago”) and valleys (the doomed “Merlin”). If “The Visit,” which also stars Roger Rees and features a tartly didactic book by Terrence McNally, occupies a sort of landscaped plateau in this terrain, its leading lady continues to tower. “I’m unkillable,” Ms. Rivera’s character says, and a line uttered with throwaway bravado stops the show.