Dougherty shot two-under 70, eight strokes off the career-best 10-under-par 62 he scored in the opening round on Thursday.
Denmark's Soren Kjeldsen shot 68 for a share of third on 11-under-par 133, while India's Jyoti Randhawa was also on 11-under but only completed 16 holes before rain halted play for the day at 7:25pm local time.
Briton Graeme McDowell (68) and Swede Peter Hedblom (68) completed their rounds and were a further stroke behind at 10-under, along with Argentina's Rafael Echenique, who managed 11 holes before the downpour.
|"It has always been one of my dreams to win the Malaysian Open." |
No Malaysian has won the national championship since its inauguration in 1962, but the second day belonged to Chia, who is only playing in the co-sanctioned European Tour and Asian Tour tournament due to a sponsor's invitation.
""I'm shaking. It has always been one of my dreams to win the Malaysian Open," Chia told reporters.
"Every year it gets tougher and tougher as it is now jointly sanctioned.
"But it's made me more excited to see my name on the leaderboard."
Return to the tour
After becoming Malaysia's first winner on the Asian Tour in 2002, Chia's career never quite took off, and he lost his tour card last season despite finishing tied fifth in Cambodia in his final tournament.
Chia subsequently regained his playing rights from qualifying school and recorded another top-five finish in last month's SAIL Open in India, which has boosted his confidence.
Dougherty was happy with his performance despite losing his outright lead as he completed his round following a two-hour suspension due to a lightning storm.
"It is still all right to shoot two under par," the Briton said.
"I played pretty well to be honest. I didn't make anything all day. It is ironic really as I didn't play much different to yesterday."
"It is easy to stall and I felt I kept going forward."
Play will start earlier on Saturday at the $2 million event, with 49 players yet to finish the second round.