Mr Chernomyrdin, who arrived in the Slovak capital, Bratislava, yesterday, is expected to sign no fewer than 12 agreements with the Slovak government, covering trade, co-operation between the Russian and Slovak central banks, science and technology, and arms production.
The deals go some way beyond anything that Russia has agreed with other Central European countries, notably the Czech Republic, Hungary and Poland. They indicate that Russia regards Slovakia as its best friend in the region.
The reason for Moscow's enthusiastic interest in Slovakia is not hard to find. Alone in Central Europe, Slovakia is unlikely to receive an invitation from Nato next July to join the Atlantic alliance in 1999.
Western governments have serious doubts about the quality of Slovak democracy under its populist Prime Minister, Vladimir Meciar, and they consequently believe that Slovakia should reform itself before earning a Nato invitation.
Russia, spotting its chance, has stepped in.
According to the Russian ambassador to Slovakia, Sergei Zotov, the Russian- Slovak arms accords could be far-reaching enough to complicate any future attempt by Slovakia and Nato to get together.
Moreover, Russia has an exceptionally strong card to play, in that Slovakia depends on the Russians for almost all its gas supplies.
However, many Slovaks are alarmed at the implications of such a close relationship with Russia. They include the head of state, President Michal Kovac, who is Mr Meciar's sworn political enemy. Liberal Slovaks would prefer to bind their country to Western institutions. The effect of Mr Meciar's policies has been to push Slovakia towards the Russian bear-hug.