Bjorn holds the clubhouse lead with his first round 66 before thunderstorms forced the opening round to be suspended. A total of 78 players will resume their round on Friday at 7.30am local time.
Chinnarat is bunched in equal second together with England's Simon Khan and Spain's Pablo Martin while Asian Tour honorary member Y.E. Yang of Korea provided his small legion of Korean fans with something to cheer about when he signed for a 68 to take a share of fifth place with England's Paul Casey and Thailand's Kwanchai Tannin.
While Bjorn has won 13 times in Europe, the 41-year-old Dane is still searching for his first win in Asia. His opening round performance at the Sentosa Golf Club has now kept up his hopes of meeting that target.
"I came here and saw the golf course, and knew that everything was about driving the golf ball well. It's not the longest golf course in the world so if you can keep it in the fairway, you can produce a score, and I did that very well today. That's only round one, so we'll work from here," said Bjorn who marked his card with six birdies against one bogey.
"I always enjoy coming to Singapore and Malaysia. You have got to pace yourself a little bit and not use too much energy through the week. It is about playing golf this week, and quite nice for the body to be feeling warm and nice out there. No cold for the old joints to get you into trouble!" added the Dane
Chinnarat, who became the youngest winner on the Asian Tour when he won his first title on home soil at the age of 17 years and five days, believes he can do well at the Barclays Singapore Open which features the world's best player, Rory McIlroy of Northern Ireland and eight Major champions.
"I feel very good. I feel very confident today on my front-nine. I hit a lot of good tee shots on the front nine. I putted well too," said the 24-year-old who mixed five birdies against one bogey on the par-four sixth.
"On this course, you've to hit the ball onto the fairways and that's what I managed to do throughout my round today," added Chinnarat.
Yang, Asia's first Major winner, was delighted to have the small Korean community following him throughout his round on the Serapong course.
The Korean did not disappoint as he signed for a 68 to stay two back of Bjorn.
"It's definitely good to see fans of your home country following you around in such a big tournament like this and under such hot and humid weather conditions. It gives me a lot of motivation," said the Korean.
Yang, however conceded that he will have to do better on the treacherous 587-yard par-five seventh as he progresses through the week.
"I drew an eight-iron on the second shot, hit it about 20-30 feet away to the right and it went towards the hazard and I ended up with a bogey. It's probably one of the worst shot I've hit this year," said Yang of his only dropped shot for the day.
Four-time Major winner Phil Mickelson of the United States had a round to forget after he signed for a 73 while three-time Barclays Singapore Open winner, Adam Scott of Australia returned with a 71.
"It was not the start I was hoping for. I had been playing really well heading into this tournament. I hit some poor shots but fought very hard to stay a couple over," said Mickelson.
This year marks the 49th staging of the Singapore Open which is co-sanctioned by the Asian Tour and European Tour.