A key obstruction to the twistor programme has been its so-called ‘googly problem’, unresolved for nearly 40 years, which asks for a twistor description ofright-handed interacting massless fields (positive helicity), using the same twistor conventions that give rise toleft-handed fields (negative helicity) in the standard ‘nonlinear graviton’ and Ward constructions. An explicit proposal for resolving this obstruction—palatial twistor theory—is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphicquantizedtwistor ‘Heisenberg algebra’, extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation.