Answer by Rory Young:
During the colonial era all zebras were white with black stripes. They are now all black with white stripes.
Seriously though, they used to be believed to be white with black stripes because the underbelly is white. They are now however believed to be black with white stripes.
Melanocyte skin cells "activate" the dark hair pigmentation. In the case of the white stripes this development is inhibited. Therefore the colour of the hair/fur is black and the white stripes are a lack of colouration.