Color constancy is the problem of how we see various shades of one color as really of one color. For instance, we see a ping pong ball as white, when it is really a gradation of shades of gray--a painter would have to use dark pigments to paint a ping pong ball as a spherical object.
Here's another example, where the A square looks darker than the B square:
The A square and B square look like they are different shades in the checkerboard above, but in the checkerboard below, they are shown to be the same shade.
This suggests that the shade of the chalkboard that we see is in fact different from what we really see. Of course, this does not amount to saying that the chalkboard is not green, but rather a different shade of green that what we seem to experience.
The Lilac Illusion however, produces an experience of green occurs from a gray experience, where there is no green to be experienced. This, coupled with the shade illusion above, suggests that perhaps the color of the Chalkboard is other than what we experience.