The sensor in an electronic camera can't actually collect color data. If you want color data out of an electronic sensor, you've got to put filters over the sensor and use electronic means to convert the information collected to color.
A one-chip camera can do this in one of two ways. The designer can put a wheel with three filters - red, green and blue - in front of the sensor, or he/she can put a piece of glass with thousands of minuscule filters on it in front of the sensor, then tell the computer that processes the information, "if you see some data from position x, which has a blue filter in front of it, put that data in the blue channel." The first way doesn't allow shooting moving subjects, the second cuts down on the resolution you can get from the sensor - though you can compensate for this by just putting a better sensor in the camera.
A three-chip camera uses a series of prisms to send the same image to three different sensors, and it has color separation filters in front of each sensor. The advantage is higher resolution. The disadvantage is the lenses have to be made for this system - the lens off a film camera or 1-chip digital won't work. Panavision's digital movie cameras use a 1-chip setup because of the lens issue: Panavision (which only rents equipment; they don't sell it) has a LOT of lenses in their inventory, and they didn't want to have to build all new ones for digital cameras.