According to the latest survey by private pollsters Hinterlaces and Keller and Company published on Friday, 45% of those asked said they would vote to keep Chavez in office.
Only 34% of the respondents said they would vote to oust him.
But the survey also found 21% of those interviewed would not answer questions as to which way they would vote.
Earlier this week, another opinion survey gave Chavez 49% backing to 41% for the opposition.
If the conservative opposition is to oust Chavez on 15 August, it needs to earn more than 3.7 million votes.
Analyst Alfredo Seller said the key for the opposition was to pull in those voters who did not approve of Chavez, but were also not thrilled by the opposition.
"If the opposition campaign manages to captivate neutral voters who are opposed to Chavez, he would be recalled, although by a very thin margin," Seller said.
About 13.8 million registered voters are set to go to the polls on 15 August.
Since the recall was set, Chavez has launched a strong campaign to crush his opponents, traveling all over Venezuela.
He has described his adversaries as ''the devil unleashed'' and warned that on the day of the recall they would ''bite the dust''.