Only 500 tickets are available for a seat aboard a train through the 57-kilometre Gotthard Base Tunnel, scheduled to become operational on the rail line linking the cantons of Uri and Ticino on June 1st.
The draw for tickets closed on Sunday after starting at the end of December, with thousands signing up for the ride into history.
Several lots of tickets have been distributed with the rest to be handed out in the coming weeks.
The public will have another opportunity to buy tickets for the first trains passing through the sub-Alpine tunnel on June 4th and 5th, when a festival is planned.
Swiss Federal Railways will start selling tickets in April for shuttle trips that are planned to run every 20 minutes through the tunnel.
The federal government has approved a budget of 12 million francs to celebrate the opening of the tunnel, starting on June 1st, 17 years after drilling under the Alps on the first shaft.
Built at a cost of 12.2 billion francs, the twin-tube tunnel lies at the heart of Europe's most important freight transport axes, linking Italy to the south with Germany and other parts of Europe.
The construction project is designed as part of a Swiss policy of transferring freight from trucks using roads through the environmentally fragile Alps to rail.
The tunnel, part of the New Rail ink through the Alps (NRLA) project, will shorten travelling distances for freight and passenger trains.
As previously announced, the Swiss government has invited 1,200 international guests for the tunnel's opening, with 300 members of the media expected.
All 246 members of the Swiss parliament and the seven members of the federal government are among the throngs of dignitaries expected.
The federal transport office has created a Gottardo 2016 website devoted to the tunnel's inauguration, complete with a second by second countdown to June 1st.