The second seed Indian bageled the sixth seed Taipei player in the opening set but eventually lost 6-0 5-7 3-6 after battling for two hours and 22 minutes.
Somdev (90) won two points more than Chen but still ended up losing the contest.
The Indian earned USD 1,460 and 15 points for his quarterfinal appearance.
With Somdev's defeat India's challenge ended at the event. Somdev had lost his doubles first round with Taipei partner Jimmy Wang.
Ramkumar Ramanathan exited after first rounds in both singles and doubles while N Sriram Balaji had lost in the singles second round of the USD 50,000 tournament.
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