I guess he was alive when the Chapel was built. From the chapel's website
The Rothko Chapel was the last and one of the most important endeavors that Dominique and John de Menil worked on together. This modern work of religious art commissioned for Houston is comparable in importance to the Chapel of the Rosary in Vence by Henri Matisse or the Chapel in Ronchamp by Le Corbusier in France.
Mark Rothko, one of the most influential American artists of the mid-century was commissioned by the de Menils and given the opportunity to shape and control a total environment to encompass a group of fourteen paintings he especially created for this meditative space. He worked closely with the original architect Philip Johnson on the plans, then with Howard Barnstone and Eugene Aubry who completed the building.
The Rothko Chapel and Barnett Newman's sculpture: "The Broken Obelisk" facing the Chapel and dedicated to Dr. Martin Luther King, Jr., have achieved world recognition as examples of the greatest artistic achievements of the second half of the twentieth century.