Hmmmm. This could be an interesting search. This Google cached page says it was the theme song of the 1933 movie, Peg O' My Heart, starring Marion Davies. Here's a quote from the page:

Shortly after Davies completed filming Peg o' My Heart, she and Hearst threw one of their much-celebrated parties - this one to celebrate his 70th birthday - at San Simeon, the lavish estate shared by the couple. The guest list of about 200 included the cream of Hollywood society. The theme was "Pioneer America," and Davies dressed as Hearst liked to see her in films - in a gingham dress and sunbonnet. The dance orchestra repeatedly played the theme from Peg, "There's a Light in Your Eyes, Sweetheart, Darling," a lilting ballad in the old Irish tradition which was destined to become even more popular than the movie. Within a short time, it was named the country's number one song.

So, we're looking for a song that was #1 in 1933, the theme song of a well-known movie. That shouldn't be hard, should it? Lyrics World usually has that sort of thing, but I don't see it. There's a 1918 song by P.G. Wodehouse called There's a Light in your Eyes, but that's not it.
-Joe Offer-