WALTHAM, Mass. — If you’re already holding tickets to a Boston Celtics game this season, consider yourself lucky. There aren’t many more left.

Only a week after putting single-game tickets on sale, the Celtics are looking at their most successful showing at the turnstiles since they left venerable Boston Garden. Celtics president Rich Gotham said season-ticket sales are up 40 percent and the team has already sold close to 80 percent of its season tickets. About 26 games are sold out, and no game has more than 1,000 tickets remaining.

After falling off the NBA map over the last five years, the Celtics are now riding a renewed wave of hope, sparked by the offseason acquisition of All-Stars Kevin Garnett and Ray Allen. Combined with returning star Paul Pierce, the Celtics are billing their new trio as a second coming of the Big Three. The last trio of stars — Larry Bird, Kevin McHale and Robert Parish — led Boston to world championships in 1981, ’84 and ’86.

“The business environment has really changed for us,” said Gotham, a Providence College graduate. “We’ve had a really hot offseason business-wise. We’re projecting to sell out most of our games this year.”

A picture of Allen, Garnett and Pierce adorns the Celtics’ Web site, and large billboards of the three stars will be popping up around Boston’s highways in the coming weeks. The team will hold its annual media day today and officials expect the largest turnout in years. Gotham said the team’s TV partner, FSN New England, will soon be renamed Comcast SportsNet and build a large presence around the Celtics that will feature half-hour shows before and after every game.

Despite the second-worst record in the NBA last season, the Celtics averaged 16,843 fans in the 18,624-seat TD BankNorth Garden. Now, with an aggressive offseason that’s seen the team’s payroll skyrocket over $55 million owed to the three stars, selling tickets, luxury suites and corporate sponsorships is an even larger priority.

“We sell tickets so we can win. Winning is the priority,” said Gotham, who added that the team will hold back about 300 tickets priced at just $10 for day-of-game sale.

The Celtics will begin their preseason workouts far from their fans. The team boards a plane and flies to Rome, Italy, on Saturday for the start of a 12-day trip that will end in London. The Celts play the Toronto Raptors in Rome and Garnett’s old team, the Minnesota Timberwolves, in London before returning to the States. The Celtics will play four exhibition games in New England, two in Boston and one each in Worcester and at the Mohegan Sun casino.

The team the fans will see will be amazingly new. Coach Doc Rivers welcomes 11 new players to camp, including recent free-agent signees Dahntay Jones and Esteban Batista of Uruguay. A year ago, Rivers led one of the youngest teams in the league through the NBA’s wars. This fall, his main goal will be introducing so many new players to each other and getting a cohesive team ready for action.

“This is a different group of guys I’m working with,” said Rivers. “(Last year) was a group of 23-and-unders, really. There wasn’t enough hours in the day with them. These guys, a lot already know how to play. Rest will be more important for this group.”

kmcnamar@projo.com