The Western Hemisphere's top diplomatic body, without a secretary-general since October, said it would hold another vote on 2 May to try to break the deadlock.
It could include another candidate in an attempt to split the vote in a sixth ballot.
"The vote has been set for 2 May. Nobody knows what's going to happen but it's possible there will be a third candidate put up," said OAS spokesman Javier Montes.
The 34-nation OAS called a two-hour recess earlier in the day after three secret ballots produced 17 votes each for Mexican Foreign Minister Luis Ernesto Derbez and Chilean Interior Minister Jose Miguel Insulza.
But two subsequent ballots also gave 17 votes to each candidate, causing visible amusement among OAS officials as the votes were counted out loud.
"This has been very tight, to say the least, it's been heart-racing," Heraldo Munoz, Chile's ambassador to the United Nations, said after the third vote.
Interim Secretary-General Luigi Einaudi told the meeting he would continue in the job before a decision by the OAS, founded in 1948 to mediate regional conflicts.
But analysts said it was urgent to find a permanent chief.
"It's getting important this decision is made. Competition is becoming too strong between Chile and Mexico. It's hurt bilateral relations," said Rafael Fernandez, vice-president of Mexico's council for international relations.
US losing clout
Neither candidate was the first choice of the US, which had backed former president Francisco Flores of El Salvador - the only Latin American country with troops in Iraq.
In past elections, the US choice has always prevailed.
"This means a new situation in the OAS, so much so that nobody knows the steps to take to resolve the problem," said Chilean political analyst Ricardo Israel.
"One thing I am sure of is that this was a very bad result from the point of view of the United States," he said, adding it suggested assistant US Secretary of State Roger Noriega was not in tune with current Latin American issues.
Former World Bank economist Derbez, 58, was the main public face of Mexico's opposition to the war in Iraq, which strained relations with Washington.
Chile's government also opposed the US-led Iraq war.
The OAS - which represents the entire hemisphere except Cuba - has been without a leader since October, when Costa Rica's former president Miguel Angel Rodriguez quit to face corruption charges at home.