It depends on your definition of _two-dimensional,_ more precisely your notion of _dimension:_
* Topological dimensions are 1. (There may be some notion of the topology of the attractor according to which it is two-dimensional, but not more than this.)
* Fractal dimensions are strictly larger than 2 (also see the other answer).
* If you look for the lowest-dimensional manifold that contains the attractor, this needs to be larger than two since you cannot have a continuous-time chaotic dynamics on a two-dimensional manifold: You need at least one dimension for temporal evolution, one for stretching, and one for folding.
Note that the last two points apply to all chaotic attractors of continuous-time systems.