The paper simulates the redistributive impact of three possible scenarios for the introduction of a basic income (BI, also sometimes called "citizens' income") in Québec. The simulations are revenue neutral at the joint provincial-federal government level. The first scenario assumes that a set of social programmes and fiscal transfers is replaced by a BI system. This does not change the marginal tax rates of the personal income tax system. These programmes and transfers include most of the personal tax credits. A second scenario also changes the explicit marginal tax rates of the personal income tax system such as to reduce the adverse redistributive impact of the first scenario. The third scenario further eliminates income support and employment insurance, such a to make the BI system more generous, and it also modifies substantially the explicit marginal tax rates of the personal income tax system through a move to a "flat-tax" system.