After more than five weeks of vicious combat that has killed probably thousands and driven hundreds of thousands from their homes, the Chechen delegation emerged from talks with Mr Chernomyrdin claiming a truce agreement that could go into force as earlyas today.
Russian officials, however, immediately dampened hopes of a breakthrough. A senior aide to President Boris Yeltsin, Sergei Filatov, doubted whether the Chechens had the authority even to begin "serious talks". A 48-hour ceasefire announced unilaterally by Moscow last week broke down immediately.
The confusion mirrors the disarray that has surrounded Russia's decision-making over Chechnya since Mr Yeltsin ordered in troops on 11 December and suggests that a bitter battle inside the Kremlin over the conduct of the war has now shifted to focus instead on the conduct of peace negotiations.
Itar-Tass news agency yesterday gave a cryptic insight into what is widely seen as a struggle not only over Chechnya but Russia's future course.
The agency quoted an unnamed "well-informed Kremlin source" as saying "the command of the operation is changing hands," and suggested a future purge of officials responsible for the debacle - "Actions of certain figures in Chechnya will not go unpunished".
Yesterday's peace talks came a day after Mr Chernomyrdin, silent and apparently sidelined during the first stage of the war, gave a television address calling for an end to bloodshed that he called "our common tragedy".
The address stopped well short of offering Chechnya independence, but did moderate Moscow's previously stridently belligerent rhetoric.
Uncertainty over Moscow decision-making is matched by doubts over whether the Chechen officials at the talks, the Justice Minister, Usman Imayev, and the Economics Minister, Taimaz Abubakarov, represent the views of Dzhokhar Dudayev, the Chechen leader, and whether even Mr Dudayev can control Chechen fighters.
Mr Abubakarov, in particular has consistently taken a more conciliatory line with Moscow than many others in the Chechen leadership.
At the same time, the government press service said "the Chechen side has not yet formed a delegation of the necessary level for holding officials talks on a peaceful settlement".
Whatever their real outcome, however, yesterday's meeting did mark the first attempt at peace negotiations since Chechen officials met a low-level Russian delegation in the town of Vladikavkaz immediately after the start of the conflict.
In Grozny, heavy fighting continued yesterday with the Chechens appearing to gain ground. There were unconfirmed reports that the rebels had recaptured the capital's railway station.
Reports that the Russians had closed the ring to the east led to speculation that the assault was entering its final stages, but the Russian posts to the west remained relaxed. Troops attempted to prevent journalists reaching the city from the east, but those coming from the west had no trouble.
Shelling and air attacks continued at high intensity. At noon, a Russian plane - believed to be an Su-23 Flogger - attacked a Western press crew about 500 metres from the Minutka roundabout, a mile south of the presidential palace.
The Russians are bringing large numbers of troops into Beslan, the airport for Vladikavkaz in neighbouring North Ossetia. During the day, little military activity is apparent but it starts with nightfall.
On Sunday, helicopters descended at dusk carrying Russian dead and wounded from Grozny.
They were unloaded, some walking wounded, some bodies strapped to stretchers, and the next wave of cannon fodder climbed aboard, a witness reported. "There were two bodies. One had damage to his face.
"The reaction of the guys going in was horror.
"The bodies had name tags. You could see a lot of people coming up to see if it was a friend."