As others have said, the pieces can be glued back together, though since it is often used to carry weight, that may not be strong enough. I would probably glue a reinforcing plate under the break, at least 3-4 inches wider than the crack line. Corian is a porous material and readily glue-able with any type glue that works on porous materials like pottery.
Or have a cabinet shop make you a replacement piece is some suitable matching color. Doesn't have to be corian either - you might choose wood and have a spare cutting baord as well. Most kitchen & cabinet shops have leftover pieces of corian or hardwoods or mica that are large enough to make a sink cover, though some of them won't want to bother with a small job like that. Ask around.
There are even online shops that will cut Corian (or other solid surface brand) to order. Here's one:
http://solidsurface.com/blog/how-to-order-corian-cut-to-a-custom-size/