ABC News' Alyssa Newcomb and Calvin Lawrence Jr. report:

(Image Credit: John McDonnell/The Washington Post via Getty Images)

In three weeks, I'll Have Another will attempt to be the first thoroughbred in 34 years to take home the Triple Crown.

All eyes will be on the Belmont Stakes in New York, where the 3-year-old chestnut could join the elite company of Triple Crown winners, including Secretariat, Seattle Slew and Affirmed.

"We're thinking Triple Crown, baby," the thoroughbred's trainer, Doug O'Neill said. "He's a special horse."

Bodemeister, the speedy second place finisher at the Kentucky Derby and the bookies' favorite to win The Preakness, will not compete at Belmont, his trainer said.

With perhaps his biggest threat out of the way, I'll Have Another will still have to overcome a number of obstacles to take home the third jewel, including little recovery time from the two top-flight races.

At 1 ½ miles, Belmont's track has been billed the "test of the champion." The Derby is 1 1/4 miles, and the Preakness is 1 1/8 miles.

The last horse to win both the Kentucky Derby and the Preakness was Big Brown in 2008, but he came up lame on the far turn at Belmont, and finished last.

"A lot of horses can handle the Derby and the Preakness, and can't handle the Belmont," Louie Roussel III, who was trainer and co-owner of 1988 Preakness and Belmont winner Risen Star, told the New Orleans Times-Picayune two years ago.

The Belmont Stakes are on June 9, giving I'll Have Another only three weeks to recover from his homestretch dash at The Preakness.

He'll  also have to compete against more horses than Affirmed, the last winner that took home the Triple Crown in 1978.

"In days gone by, we didn't have a full field come back in the Preakness and the Belmont," Graham Motion, the trainer of Went the Day Well and last year's Derby winner Animal Kingdom, told the Wall Street Journal this week.

Affirmed faced six horses in the 1978 Preakness. Eleven competed in Saturday's race.

Despite the obstacles, I'll Have Another's jockey Mario Gutierrez expressed faith in the horse's ability to win.

"He just keeps proving people wrong," he said. "I'm so happy for him because he's such a great horse. He has a tremendous kick in the end."