Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β in the following way. Hinge the parts of α like a chain along the perimeter of α, then fix one of the parts and without turning the pieces over, rotate the remaining parts about the fixed part to form β in such a way that the entire perimeter of α is in the interior of β and the perimeter of β consists of the dissection lines formerly in the interior of α . In this paper we discuss a special type of Dudeney dissection of convex polygons in which α is congruent to β and call it a congruent Dudeney dissection. In particular, we consider the case where all hinge points are interior to the sides of the polygon α. A convex polygon which has a congruent Dudeney dissection is called a chameleon. We determine all convex polygons which are chameleons.