In late March, from his cell in a Turkish jail, Abdullah Ocalan issued an order: the 2,000 fighters of his outlawed Kurdistan Workers' Party (PKK) were to withdraw from Turkey and move south into Iraq. Now, as they go, they may be exporting a problem to Iraq and Iran and Syria, but they are giving Turkey a remarkable opportunity.
Three decades of sporadic PKK insurgency have killed at least 40,000 people, and left the country's south-east badly underdeveloped. In prison since 1999, Ocalan has, he says, changed his thinking and now favours non-violence; he has been negotiating with the government of the prime minister, Recep Tayyip Erdogan.
Of Turkey's 75 million people, almost a fifth are Kurds. The PKK has never spoken for all those 15 million people, but PKK violence has poisoned relations with the majority. Turkish politicians are well supported when they cite PKK terrorism to argue against Kurdish interests.
But almost 20 per cent is too big a minority to suppress with impunity. Kurdish resentment of the government, and indeed support for the PKK, vary in proportion to majority attitudes towards the minority.
It is no coincidence that Ankara's talks with Ocalan have borne fruit just as Turkey is rewriting its constitution. The main purpose of this exercise, many suspect, is to beef up the presidency from ceremonial to executive status, since Mr Erdogan aspires to accede to it.
But this is also a golden opportunity to heal the breach with the Kurds. Here language policy is both practical and symbolic; some recent liberalisation on the teaching of Kurdish and its use in some courts, and in political campaigns, are welcome, but all this and more deserves to be entrenched in the constitution.
A 12-member commission on the new basic law has not reached consensus, and Kurdish rights are just one of the issues in play. A draft that guarantees new Kurdish rights will not necessarily be popular outside of the country's Kurdish heartland, so making this come out right will challenge even Mr Erdogan's formidable skills. But there is hope here of a just and enduring new arrangement.
But what, meanwhile, of those tough PKK fighters? Iraq's central government does not welcome them, and even Iraqi Kurdistan - which has its own well-trained military - will have little use for them. Some may drift into Syria, or to Iran, where local Kurds have a wary ceasefire with the Tehran government.
Dissolving the PKK is tomorrow's problem. Today's concern, for Mr Erdogan and all of Turkey's political class, is to define and implement a just new balance between the majority and the Kurds.