  The twist-deformed conformal algebra is constructed as a Hopf algebra with
twisted co-product. This allows for the definition of conformal symmetry in a
non-commutative background geometry. The twisted co-product is reviewed for the
Poincar\'e algebra and the construction is then extended to the full conformal
algebra. It is demonstrated that conformal invariance need not be viewed as
incompatible with non-commutative geometry; the non-commutativity of the
coordinates appears as a consequence of the twisting, as has been shown in the
literature in the case of the twisted Poincar\'e algebra.
