The Chilean Supreme Court could rule within a month on Peru's request for former President Alberto Fujimori to be extradited, officials have said.
Mr Fujimori recently tried and failed to win a seat in Japan's parliament
The court will either confirm or reject a previous ruling that he should not be sent back to face charges in Peru.
Mr Fujimori, Peru's leader from 1990 to 2000, is accused of human rights abuses and corruption - charges he has denied.
Currently under house arrest, he has been in Chile since arriving from Japan unannounced in November 2005.
The head of the Supreme Court's second chamber, which heard arguments from Peruvian government lawyers and Mr Fujimori's legal team, said the judges would probably begin discussing the case on Monday.
Asked how long their deliberations would last, Judge Alberto Chaigneaux said it would probably be less than four weeks.
In July, a Chilean judge blocked Mr Fujimori's extradition, saying the said the evidence presented by the Peruvian authorities was unconvincing.
This prompted an appeal by Peru.
In 2000, Mr Fujimori, the son of Japanese immigrants in Peru, fled to Japan amid a bribery scandal.
The Japanese authorities repeatedly refused requests by Peru to extradite him on charges including directing death squads, illegal phone tapping and corruption.
In November 2005, he travelled to Chile, hoping to launch a new bid for the Peruvian presidency in 2006 elections, only to be arrested at the request of Peruvian authorities.