A dapper gentleman (Cary Grant) strolls serenely through the streets of the city, admiring the Christmas decorations and the smiling faces of children. He seems to be wandering around doing good deeds for others, almost magically appearing at the right place and time. When he observes the beautiful but sad Julia (Loretta Young) converse with her old friend Prof. Wutheridge (Monty Woolley), he takes a serious interest in helping her. Feigning an old aquaintance, he gets more information from the professor, who's unsure if they've ever really met, but guardedly tells the gentleman about Julia's troubles. As they part, Wutheridge wonders who the fellow really is.
When she arrives home, Julia finds her husband Henry Brougham (David Niven) the bishop of the local diocese, in a heated argument with the chair of the cathedral committee, Mrs. Hamilton (Gladys Cooper), a wealthy but domineering old woman. Henry has a dream of building a new cathedral, and has come to depend on Mrs. Hamilton's financial support. Unfortunately, she demands that the cathedral be built as a monument to her late husband, a situation Henry cannot accept. Later, he argues with Julia, and its obvious that their marriage is strained. Harried and harrassed, Henry is at his wit's end, and retiring to his study he prays for guidance. Turning to leave, he is surprised to find that the dapper gentleman has somehow appeared in his study. Telling Henry that his name is Dudley, he reveals his true nature: he's an angel, and he's come in answer to Henry's prayer.
Despite Henry's doubts, Dudley quickly charms his way into Henry's life, becoming a favorite of his maid, his daughter, and even his wife Julia, all the while preventing Henry from telling anyone what Dudley claims to be. Julia begins to enjoy Dudley's company, being completely charmed by his ability to do seemingly everything well. Meanwhile, Henry gets no closer to building his cathedral, and becomes increasingly angry with Dudley for taking over his family. A confrontation looms, and Henry decides to submit to Mrs. Hamilton's demands in order to speed things along, get his old life back, and get rid of Dudley.
Confronting him, Henry tells Dudley he can leave; his prayer had been answered. Dudley's not so sure however. What does Henry really want: the cathedral, or Julia's happiness? Enraged, Henry demands that he get out of his life at once, and as Dudley departs with a smile, he admonishes Henry not to let Julia see him this angry. Later, visiting Professor Wutheridge, Henry confesses that he's probably lost Julia to Dudley, and is surprised to find that he can actually tell the professor about Dudley's true nature. Wuthridge reminds Henry that he has an advantage over an angel: he is a mortal man, and Julia is a mortal woman.
Facing Dudley one last time, Henry tells him that Julia means more to him than life itself, and he's willing to fight Dudley no matter what may happen. Relieved the Henry has gotten his priorities straight at last, a beaming Dudley tells Henry that he's leaving, and that his prayers have been answered. Confused, Henry disagrees. "I prayed for a cathedral", he says.
"No Henry, you prayed for guidance," says Dudley. "That has been given to you."
Dudley has shown him the true value of his life, and has brought Henry and Julia back together. He departs, and takes with him all memory of his existence. None of the people he's helped remember him at all, but all realize that their lives have been changed. As they gather in church for Henry's Christmas Eve sermon, Dudley stands outside, unrecognized. He smiles, and walks off into the city.