The Behaviour and Attitudes poll for tomorrow's Sunday Times was conducted over a 12-day period between 30 March and 11 April last.
The margin of error is plus or minus three percentage points.
Compared to the last similar poll published in March the latest findings put Fine Gael up seven points to 29%.
There is no change for Fianna Fáil at 28% while Sinn Féin is down five points to 18%.
Labour is down one point to 5%, as is the Independent Alliance.
The Greens remain at 2%.
Solidarity / People Before Profit are up one point to 3%; this includes 1% for the Socialist Party.
The Social Democrats are up one point to 2% and all other independents are up two points to stand at 10%.
The poll also takes account of the Taoiseach's high profile visit to Washington for St Patrick's Day.
And that factor, along with the publicity around the future leadership of the party may also be contributing to the seven-point increase in support for Fine Gael.
The poll also shows an eight-point rise in Taoiseach Enda Kenny's personal rating to 35%. That still leaves him trailing other party leaders but it might spur more speculation within Fine Gael on whether it might influence the timing of his departure.
Overall, the result puts Fine Gael ahead of Fianna Fáil for the first time since June 2016 in this sequence of polling.