Hamas would get 28.6 percent of the vote compared with 27.9 percent for the rival Fatah faction of Western-backed president Mahmud Abbas if elections were held today, according to the survey by the Jerusalem Media and Communications Centre.
It marks the first time that an opinion poll has placed Hamas in front of Fatah, which it ousted from the Gaza Strip in deadly fighting in June 2007.
Hamas scored an upset victory in January 2006 parliamentary elections, defying opinion poll predictions which had seriously underestimated the Islamist vote.
Ironically Thursday's poll found that Hamas has stronger support in the Israeli-occupied West Bank, still administered by Abbas, than it does in its own Gaza bastion.
In Gaza, the poll put Hamas at 28 percent against 33.6 percent for Abbas' Fatah. In the West Bank, the poll gave Hamas 29 percent support against 24.5 percent for its rival.
The balance was shared by a myriad of smaller parties.
Some 27.7 percent of those questioned said they trusted Hamas, compared with 26 percent for Fatah.
The poll found that Hamas prime minister Ismail Haniyeh, who Abbas dismissed after the Islamist takeover of Gaza, is the most trusted Palestinian politician with 21.1 percent support, far ahead of the incumbent president with 13.4 percent.
When asked who won the war in Gaza, 53.3 percent of people in the West Bank said Hamas, compared with 35.2 percent in Gaza.
The pollsters surveyed a sample of 1,198 people -- 758 in the West Bank and 440 in Gaza -- and gave a margin of error of plus or minus three percent.