Limited types of radioactive molecules (RM) can be made inside hot-cavity targets at ISOL facilities like TRIUMF. However, extreme conditions in these targets present formidable unsolved challenges to efficient production and delivery of RM's. Here we propose using RFQ gas-reaction cells to produce RM from radioactive ion beams (RIB) by room temperature RIB-gas chemical reactions at eV energies. Two options are possible: (1) using an ion reaction cell (IRC) that is a linear RFQ ion guide and reaction cell used as an 'on-line ion source', and (2) using the ARIEL RFQ cooler-buncher (ARQB). RFQ gas-cells are a controllable and efficient method to produce RM from chemical reactants that cannot be used in ISOL targets. This 'online chemistry' offers a way to enable groundbreaking Beyond Standard Model (BSM) physics research, using a wide diversity of new rare and exotic RM beams that would be difficult or impossible to produce in hot-cavity targets.