NEW DELHI -- Defying all the conventional wisdom about Indian television viewers -- notorious for dogged allegiance to campy soap operas that pitted idealized brides against scheming mothers-in-law -- the hottest show on TV today is a progressive, heartwarming drama about a plucky little girl caught up in an illegal child marriage.

Called Balika Vadhu, or "Child Bride," and set in rural Rajasthan, where marrying off daughters before they hit puberty is still a common practice, the show has...