Iceland's anti-establishment Pirate Party has been asked by the president to try to form a new government, following October's snap elections.
President Gudni Johannesson made the announcement after talks with Pirates head Birgitta Jonsdottir.
The Pirates, who vowed radical reforms, came third in the elections in which no party won an outright majority.
Two earlier rounds of coalition talks involving first the Independence Party and then the Left-Greens failed.
"Earlier today, I met the leaders of all parties and asked their opinion on who should lead those talks. After that I summoned Birgitta Jonsdottir and handed her the mandate," President Johannesson said on Friday.
Ms Jonsdottir said afterwards she was "optimistic that we will find a way to work together".
In the elections, the Pirate Party - which was founded in 2012 - more than tripled its seats to 10 in the 63-member parliament.
The election was called after Prime Minister Sigmundur Gunnlaugsson quit in April in the wake of the leaked Panama Papers, which revealed the offshore assets of high-profile figures.
The Pirates want more political transparency and accountability, free health care, closing tax loopholes and more protection of citizens' data.
Opponents, however, say the Pirate Party's lack of political experience could scare off investors and destabilise Iceland's recovering economy.