The Macedonians jumped through a lot of constitutional hoops to keep their end of the bargain on January 11, 2019, Their parliament officially changed the country's name to 'North Macedonia'.
So the Greeks got what they wanted, and now it is the Greek parliament's turn to ratify the deal and lift its ban on 'North' Macedonia joining Nato and the EU.
But no. A small ultra-nationalist party called the Independent Greeks, whose seven seats Prime Minister Alexis Tsipras depended on for his majority in parliament, walked out of the coalition on January 13.
Tsipras has betrayed Greece, they say. No foreigners should be allowed to use the sacred Greek name of Macedonia, even in the phrase 'North Macedonia', and what those foreigners really secretly want is to take over the whole of northern Greece.
So Tsipras now has to hold a vote of confidence, and if he loses it, there will have to be an early election.
He may well lose it, because most of the people in the main opposition party, New Democracy, are also paranoid nationalists. Or more precisely, they know that paranoid nationalism is the way to maximise the right-wing vote.
Some of them are privately quite reasonable men and women, but they know what they have to say to win, and they will say it.
How has this nonsense come to dominate the politics of two entire countries for more than two decades?
When the old Communist regime in Yugoslavia lost power in 1991 and the six republics that made it up became independent countries, the southernmost one was called the Republic of Macedonia.
It came by the name honestly. From the Roman Empire 2000 years ago, down to the Ottoman Empire only a century ago, its territory was always part of a larger province called Macedonia. No other country was using the name, so independent Macedonia kept it.
There was, however, a region in northern Greece that also used to be part of that province, and also called itself Macedonia. No harm in that — the people in the Republic of Macedonia weren't claiming that the Greek region called Macedonia belonged to them. But the Greeks insisted they were, and wouldn't let them join any organisation that Greece belonged to.
So the Republic of Macedonia was frozen out of Nato and the European Union (and all the EU's subsidies for post-Communist countries in eastern Europe).
It only got a seat in the United Nations by agreeing to call itself the "Former Yugoslav Republic of Macedonia" (FYROM) for UN purposes. And the foolishness dragged on for a generation.
The Macedonians themselves — sorry, the 'North Macedonians' — eventually developed their own ultra-nationalist crazies who insisted they were the true heirs of Alexander the Great. Skopje, the capital, is littered with monuments and statues extolling him, put there by the previous government basically to yank the Greeks' chain.
It's not clear why you would want to claim descent from Alexander the Great, whose main achievement was conquering a lot of countries, killing a lot of people, and dying at 30, but then the people of Mongolia take pride in having Genghis Khan as an ancestor.
At any rate, the Macedonians did what they did, and the Greeks rose to the bait. It was really ugly for a while.
But finally the wheel turned and both countries ended up with grown-ups in charge at the same time — Alexis Tsipras in Greece and Zoran Zaev in Macedonia.
Both are social democrats who have other fish to fry, and just want to get rid of this issue that the nationalist right exploits endlessly. It hasn't been easy but they are almost there.
Zaev had to hold a referendum on the deal in Macedonia, and got 90 per cent 'Yes' votes — but the nationalists boycotted the ballot, and so invalidated the outcome because fewer than 50 per cent of potential voters took part.
That meant Zaev had to get a two-thirds majority in parliament instead, which required him to bribe some shady members of parliament with amnesties for their alleged crimes.
Tsipras will face an uphill fight to win a confidence vote, and if he loses that, he may also lose the election. He has spent a lot of his political capital in his struggle to rescue Greece from its financial plight.
These two men deserve to succeed. Maybe they will.
Gwynne Dyer's new book is Growing Pains: The Future of Democracy (and Work).