Dunga's Brazil, who will be looking to atone for their poor 2014 World Cup, meet Colombia, Peru and Venezuela in Group C.
June 17 marks the clash between Brazil and Colombia in a repeat of their quarter-final at the World Cup.
Brazil won that clash 2-1, but it was Juan Camilo Zuniga's challenge on Neymar that caused controversy and left the Brazil star with a fractured vertebra.
Both Brazil and Colombia, ranked in the world's top 10, will be expected to progress from the group stages.
Peru and Venezuela are ranked 54th and 85th respectively.
Group B also pits two powerhouses against one another, with Argentina and 2011 champions Uruguay set to do battle.
That match will be played in La Serena on June 16.
Paraguay and Jamaica, the latter were invited, are also in the group.
Tournament hosts Chile were given a good draw in Group A, which includes Mexico, Ecuador and Bolivia.
Jorge Sampaoli's men open the event with a clash against Ecuador in Santiago on June 11.
Mexico coach Miguel Herrera, whose team were also invited, had wanted to avoid Chile but got no such luck.
Group winners and runners-up will progress, as will the two best third-placed teams.
