The event, being held for the third year running, expresses the pride and confidence of one of the city's most active foreign communities. Out of all proportion to its size, Ireland is leading the way in doing business with Russia.
Five years ago, apart from diplomats, Conor O'Clery was about the only Irishman in the Russian capital. The correspondent for the Irish Times, he called his book An Irishman in Moscow because it was such a novelty then. Now there are 230 Irish in the city and 500 in Russia, mostly working as managers in the retail trade.
When he is not at choir practice, Mr Carey works as a buyer for Irish House, a huge supermarket on New Arbat Street run jointly by Aer Rianta, the operators of Shannon airport, and a Russian partner. On the other side of town is the Garden Ring supermarket managed by Colm Fitzsimons for the Irish firm of Coughlan, Flannery and Pratt. 'There's a healthy rivalry between us,' jokes Mr Fitzsimons, 'but actually there's loads of room in Russia for everyone.'
The supermarkets and other Irish-run shops and bars have changed the face of Moscow. Before, under Communism, foreigners went to special hard-currency stores stocked with Russia's choicest food as well as imported goodies while Russians queued in their own shops for lumps of fat and rotten cabbage. Helped by the Finns, Germans and Swiss who also have shops here, the Irish have broken down that Soviet apartheid. Now, regardless of nationality, whoever has sufficient roubles can buy Mr Carey's cornflakes or fish fingers from Mr Fitzsimons.
An ever-increasing proportion of customers are well- heeled Russians. Some of the Russian staff at the Garden Ring supermarket, who used to work in a Russian food shop previously on the site, cannot quite get used to this. 'We had one customer,' said Mr Fitzsimons, 'who got out of a Mercedes with a mobile telephone and a wife in a fur coat. And the old lady who mops the floor for us said to him: 'I hope you've got money to be coming in a place like this.' '
The shops, which employ cheap local labour and sell goods at very high prices, are raking in money to such an extent that the jovial Irish, who will talk freely about almost any subject, decline to discuss profits. But to reap these rewards, they are taking risks that other businessmen, including the timid British, find too off-putting. One problem is that Russia still lacks the legal framework and stable tax system needed to make entrepreneurs feel really secure. The other is the mafia. The Irish leave their Russian partners to handle the gangsters for them.
The Irish are in buoyant mood as St Patrick's Day approaches. Three years ago, when the shops sponsored the first parade, bewildered Russians looked at the floats and banners going through the city and assumed it was a political demonstration. But now everybody knows about the Irish spring festival, which coincides this year with Shrovetide in the Russian Orthodox church calendar.
The day will begin with Mass in the Church of St Louis, a beautiful old church in the shadow of the security police headquarters on Lubyanka Square which was attended by Poles and a few diplomats from Catholic countries until the Irish came along to swell the congregation. Then will come the parade. Shamrock and fiddlers are being flown from Ireland and the Guinness will be dyed green. The Moscow Irish have not yet got as far as dyeing the river green as their cousins do in Chicago but no doubt this is only a matter of time.