Having beaten Kenichi Tago on Wednesday the Chinese, who is aiming for a second title in three years, followed it up with a hard-fought win against Vittinghus.
Chen had to come from a game down before he could secure victory in Group A, the world number two winning 13-21 21-10 21-9 in 57 minutes.
Tago was well on his way to putting his disappointment behind him, leading 21-9 11-3 versus Son Wan-ho before the South Korean was forced to retire in the second game with a hamstring injury.
His win means Friday's clash with Vittinghus will decide who joins Chen in the last four, with Son playing no further part.
It is just as close in Group B, where Kidambi Srikanth is already guaranteed a top-two place after his 21-18 21-13 win over Tommy Sugiarto, a defeat that sees the latter eliminated.
That leaves Kento Momota and Jan O Jorgensen battling for the final place. The pair met on Thursday with Momota coming from a game down to win 20-22 21-18 21-12.
"I feel much better about my game in general," said Momota. "In the end I had the stronger stamina and I worked at avoiding any mistakes.
"Being patient and careful helped me to outplay him.
"After yesterday's loss this win will enhance my performance, as I knew I need to play aggressively to eventually win today and going forward."
Momota faces Sugiarto in his final game, while O Jorgensen meets Srikanth.
In the women's draw world number three Wang Yihan is out of the competition after being forced to withdraw from her Group B match with Tai Tzu Ying through injury.
The Chinese player was losing 21-12 11-8 when the decision was made, and she will not contest her final match with Ratchanok Intanon.
Intanon could not have reached the semi-finals of the competition either after her second defeat of the group, losing 21-15 16-21 21-12 to Japan's Akane Yamaguchi.
Meanwhile, in Group A, Saina Nehwal beat Sung Ji-hyun 21-12 21-18 to book top spot, while Bae Yeon-ju knocked world number two Wang Shixian out with a 21-17 21-17 win.