An electronic device may be provided with a display. Backlight structures may be used to provide backlight for the display. The backlight structures may include a light guide plate. A rectangular ring-shaped chassis may have a rectangular opening that receives the light guide plate. One or more edges of the chassis may be provided with an array of notches that receive light-emitting diodes or other light sources. The light sources may launch light into edge portions of the light guide plate. The chassis may include a first plastic structure such as a light reflecting structure formed from a material such as white plastic. The first plastic structure may surround two or more peripheral edges of the light guide plate. The chassis may also include a second plastic structure such as a light blocking structure formed from a material such as black plastic that helps prevent light leakage.