In Chile
Quiroga participated in the military actions of the conquest of Chile, during the first part of the War of Arauco, coming to be one of the most important captains of the district. From 1548 he held a number of important posts in the administration in Santiago. Three times he was mayor, amongst other duties.
He married Inés de Suárez, the famous mistress of Pedro de Valdivia, when the Viceroy of Peru at the time ordered that Valdivia end the scandalous relationship or face excommunication.
At the death of Valdivia at the hands of the Mapuches at the Battle of Tucapel, the citizens of southern Chile followed the instructions of his will and announced Francisco de Villagra as their leader. However, in Santiago, the ruling cabildo ignored these recommendations and proclaimed Quiroga as governor. It was thus that there were for a time two governors in Chile: Villagra in the south and Quiroga in the north. The situation ended upon the return of Villagra from the southern war zone to reclaim his right to govern. The cabildo awarded him this right and obliged Quiroga to relinquish his power, which Quiroga grudgingly did.
In 1565, the Viceroy Lope García de Castro sent reinforcements from Peru under the command of general Jerónimo de Castilla. Castilla had orders to arrest Pedro de Villagra (the uncle of Francisco who had risen to the post of governor while protected by the previous Viceroy), and put Quiroga in his place. In these circumstances, Villagra saw that he was too weak to defend his title, so he ceded his power to Quiroga and went to Peru.
Read more about this topic: Rodrigo De Quiroga