The aim is to bring these two long-time enemies together in a power-sharing arrangement in which they will jointly run Northern Ireland, with limited input from smaller nationalist and Unionist parties.
Republicans and fundamentalist loyalists are not, to put it mildly, a natural fit for a coalition government, and everyone knows that bringing them together is a formidable task which will not be achieved this year.
Nonetheless, the IRA's promise to disarm and cease illegal activities is already producing a sense of new possibilities, assuming these objectives are accomplished and verified.
This week the long process of re-establishing political engagement got off to a promising start, with Sinn Fein palpably eager to negotiate and Mr Paisley adopting a cautious wait-and-see stance.
This was so different from his traditional, famously rejectionist instincts that it has strengthened the sense that he will eventually go for a deal that will install him as Northern Ireland's First Minister.
Unionists have often said that the IRA's possession of weaponry was the greatest obstacle to co-operation with Sinn Fein, so there is a prospect that the disarmament of republicanism can open a new political era.
An attempt last year to arrange a Sinn Fein-DUP deal came tantalisingly close to success, but finally fell apart on the republican rejection of Mr Paisley's demand for photographs of arms being decommissioned.
The IRA continues to rule out photography, but it has agreed that the decommissioning inspector, the Canadian General John de Chastelain, will be accompanied by a priest and a minister as witnesses. Mr Paisley and his party continue to ask for pictorial evidence, but the negotiations which led to this point were between Tony Blair and republicans. The DUP was not involved in the lead-up and was therefore not in a position to make such a demand.
The theory is that witnessed decommissioning, followed by a credible period of IRA inactivity, will generally transform the political atmosphere and specifically impress Mr Paisley.
An optimistic scenario is that weapons decommissioning could be complete by September. The Government is hopeful of starting talks in that month, but initially these are not expected to take the form of full-scale negotiations.
It is accepted that Mr Paisley is not about to rush into negotiations, and will require some months of proof that the IRA has halted illegal activity.
It may be that by January a monitoring body, as well as the security forces, will be authoritatively reporting that all traces of republican illegality have now vanished.
Such a clean bill of health would mean that Mr Paisley would then come under pressure to do business with Sinn Fein. Certainly London would be urging the DUP to accept that republicans have established a new set of bona fides, and are fit for government.
If real negotiations open in January, or soon afterwards, the parties can be expected to spend several months thrashing out what changes, if any, should be made to the Good Friday Agreement, which set up the Belfast Assembly.
Republicans will probably push hard for the Assembly's remit to be extended to include policing and security matters.
A successful outcome to talks is likely to be followed by Assembly elections. This means that a new administration is unlikely to be established before next autumn at the earliest.Reuse content