Santiago

City · 1541 CE · in South America

Capital of Republic of Chile (1812–today).

Alba Iulia (c. 1542 CE): Capital of Eastern Hungarian Kingdom (1542–1570), Principality of Transylvania (1572–1692).
Tunja (1539 CE): Capital of Granadine Confederation (1859–1862).
Bogotá (1538 CE): Capital of Gran Colombia (1822–1831), Republic of New Granada (1834–1858), Granadine Confederation (1859–1862), and 2 more.
Sucre (1538 CE): Capital of Bolivia (1825–today).
Asunción (1537 CE): Capital of Paraguay (1811–today).
Buenos Aires (1536 CE): First founded by Pedro de Mendoza in 1536 and refounded in 1580 by Juan de Garay; capital of the Viceroyalty of the Río de la Plata and of Argentina.
La Paz (1535 CE): Capital of Republic of Baja California (1853–1854).
Lima (1535 CE): Founded by Francisco Pizarro as the "City of Kings" in 1535, Lima became the capital of the Viceroyalty of Peru and of independent Peru.
Quito (1534 CE): Capital of Republic of Ecuador (1840–today).
Thanjavur (c. 1534 CE): Capital of Nayaks of Thanjavur (1534–1673), Thanjavur Maratha Kingdom (1677–1799).

Around the same time and place

Arauco War (c. 1536–1818 CE): Long-running conflict between the Spanish and the Mapuche of southern Chile, who kept their independence south of the Biobío River.