The Foreign Office is treating the visit with due priority. But in terms of Russia's security policies, Mr Chernomyrdin's trip to Poland last week may prove to be more significant. For, four years after the collapse of Communism in Russia, the former colonial power has still not worked out its relationship with the East European countries.
"One cannot choose one's neighbours, but we can be good neighbours": this was the conclusion offered by the Speaker of the Polish parliament after the Russian Prime Minister's discussions in Warsaw. His feelings are shared by most other East Europeans: while still resentful of Moscow's colonial past, all the countries of the region realise that better relations with Russia remain a necessity. Yet the problem for most of the region's governments is that, although Russia is now keen on forging links, the Kremlin's interests remain diametrically opposed to those of Eastern Europe.
When Communism collapsed, the West advised Eastern Europe not to rush into dismantling its co-operation agreements with the Soviet Union. The East Europeans, however, did precisely that, and for very good reason: quite apart from the fact that the structures imposed by the Kremlin at the end of the Second World War were hated by all, maintaining them precluded any chance of serious economic reform. Comecon, the structure that was supposed to regulate economic exchange in the Communist bloc, amounted to little more than a medieval bazaar in which second-rate economies transacted barter deals and cheated on each other. And the Warsaw Pact was a unique example of a military alliance that, far from protecting Eastern Europe against an external enemy, was used twice to invade the territory of its own member states. Dismantling Comecon and the Warsaw Pact was, as Marx would have said, a "historic necessity".
Over the past five years, all the East Europeans have transformed their economies from total dependence on Russia to a more level-headed approach that emphasises the quality of goods traded. This shift has brought Russia benefits, too. The collapse of Comecon meant that Russia could charge world market prices for its oil and natural gas, earning it hard currency. And depriving Russia of its ability to dump substandard goods on captive East European markets forces Russian enterprises to become more competitive.
There is little doubt that severing relations with Moscow was something the East Europeans did with great relish: given the historic legacy, anti- Russian feelings are almost instinctivethroughout the region. Nevertheless, it is wrong to assume that the East Europeans engaged in Russia-baiting for its own sake; countless local governments, for instance, have agonised over what should be done with the myriad Soviet monuments that dotted their landscapes. Furthermore, while Western goverments talked a great deal of their commitment to Russia, the East Europeans talked less but did more.
As every Russian citizen knows, getting a visa for a trip to the West remains a bureaucratic nightmare. But they travel in their hundreds of thousands to Eastern Europe, often needing little more than a passport. In almost every East European capital, citizens of the former Soviet Union engage in petty trade and, quite often, petty crime. But few of them are ever arrested or deported and nobody knows how many illegal Russian immigrants Eastern Europe now contains. All in all, the East Europeans have proved that they are ready to disregard the scars of history.
In public, Moscow claims to have done the same: the East Europeans are treated with all the respect due to fully independent states. But the reality is that Russia's officials have found it very hard to regard the region as simply another part of the European continent.
In Warsaw, Mr Chernomyrdin said he was "perplexed" by Poland's desire to join Nato quickly. This is far from being just an isolated opinion: almost without exception, all of Russia's politicians, from the most hard- line Communist to the greatest Western admirer, oppose the extension of the Western security alliance farther east. Their arguments vary but the message is invariably the same: if the East Europeans join Nato, this will be perceived as a hostile move in Moscow. The Russians are far from accepting the irretrievable loss of Eastern Europe.
The reason is partly psychological. The Soviet empire collapsed with little violence, and quite suddenly. Many ordinary Russians find it simply impossible to understand how and why this happened, and they resent what they consider to be the East Europeans' ungrateful behaviour. Neither they nor their leaders can get used to the idea that the disintegration of the empire might be a liberating experience for Russia itself. The men governing Russia today know that in economic and political terms, they are too weak to influence European developments. An army that needed months to subdue bands of Chechen fighters is hardly in a position to contemplate another thrust into Europe. Yet Russia's politicians also instinctively believe that their country's weakness is a temporary affair and that meanwhile it is not in Moscow's interest to accept any deal consolidating Western influence in Eastern Europe. Maintaining the status quo is the main reason behind Russia's current opposition to Nato's enlargement.
Moscow has consistently indicated that it is prepared to challenge the West if it seeks to enter the Russians' "sphere of influence". For instance, the Russians claim to harbour a "historic affinity" with the Serbs. Yet nothing is further from the truth: throughout their history, the Slavs of the Balkans have survived despite Russian scheming in the region, not because of it. Moscow's involvement in the Balkans is a marriage of convenience, intended to remind the West that it cannot make progress in former Yugoslavia without Russian support. Russian troops were introduced around Sarajevo last year simply to reinforce this message.
For the moment, both the East Europeans and the West pretend that such difficulties can be papered over. Poland has signed a series of economic co-operation agreements with Russia, and other neighbours are keen to revamp their relations with Moscow. But no amount of bonhomie can solve Europe's long-term problem. Russia's main objective - maintenance of the status quo - is no longer acceptable, either to Eastern Europe or the West.
Nato's eventual enlargement farther east is inevitable, partly because without it the Western alliance will become irrelevant to its most important European member states. The Foreign Office will be playing its part this week, by concentrating on forging institutional links with Russia - in particular, to lock Moscow into co-operation with Nato. But it should make clear to Mr Chernomyrdin that co-operation now requires a change of attitude in the Kremlin. Moscow's main enemies are no longer in the West; they are in Russia itself.
The author is Director of Studies at the Royal United Services Institute in London.