The poll of 2612 registered voters, conducted by the US firm North American Research, showed 57% favoured retaining Chavez in office, 41% wanted him removed and two per cent were undecided.
If 3.75 million voters - the number who voted for Chavez in 2000 - vote against him on 15 August, he will step down and a new presidential election will be held.
According to Venezuela's constitution, if Chavez had lost a recall held after 19 August, his vice-president would have been the president until presidential elections in December 2006.
But since the recall referendum is being held on 15 August, the constitution dictates elections within 30 days if Chavez loses.
Chavez, a leftist ex-paratrooper, was ousted in April 2002 in a short-lived military coup that visibly pleased the United States, which quickly moved to recognise and deal with the new transitional government.
But the coup fell apart within 48 hours and Chavez was returned to power after his old army unit rallied other military companies to his defence.
Though Washington insisted it had no part in or advance knowledge of the coup, Chavez accuses the United States of meddling in its politics and instigating opposition against him.
Venezuela, a member of the Organisation of Petroleum Exporting Countries (OPEC), is a key US oil supplier.