Ethnic roots of Chilean people are mainly indigenous but there is also an importante minority coming from European and Middle Eastern countries.

The total population of Chile is approximately 18 million in a total area of aboout 756,000 km2.

Scholarly estimates of the white population in Chile vary dramatically, ranging from 20% to 52%. According to a study by the University of Chile about 30% of the Chilean population is Caucasian, while the 2011 Latinobarómetrosurvey shows that some 60% of Chileans consider themselves white.

In fact, because indigenous ancestry is considered inferior many mixed people prefer to forget about their native roots. Therefore, the real number is more likely closer to 30% than 60%.

That means that at least 70 of the population of Chile have some native origin, mainly Mapuche. People that declare themselves as indigenous are about 1 million, of which more than 90% are Mapuche. They live in the south and in the larger cities.

During colonial times in the 18th century, an important flux of emigrants from Spain populated Chile, mostly Basques, who vitalized the Chilean economy and rose rapidly in the social hierarchy and became the political elite that still dominates the country. An estimated 1.6 million (10%) to 3.2 million (20%) Chileans have a surname (one or both) of Basque origin. The Basques liked Chile because of its great similarity to their native land: similar geography, cool climate, and the presence of fruits, seafood, and wine.

Chile was never an attractive place for European migrants in the 19th and 20th century simply because it was far from Europe and difficult to reach. Chile experienced a tiny but steady arrival of Spanish, Italians, Irish, French, Greeks, German, English, Scots, Croats, Jewish and Palestinian migrants (in addition to immigration from other Latin American countries).

The original arrival of Spaniards was the most radical change in demographics due to the arrival of Europeans in Chile, since there was never a period of massive immigration, as happened in neighboring nations such as Argentina and Uruguay. Facts about the amount of immigration do not coincide with certain national chauvinistic discourse, which claims that Chile, like Argentina or Uruguay, would be considered one of the "white" Latin American countries, in contrast to the racial mixture that prevails in the rest of the continent. However, it is undeniable that immigrants have played a major role in Chilean society. Between 1851 and 1924 Chile only received the 0.5% of the European immigration flow to Latin America, compared to the 46% received by Argentina, 33% by Brazil, 14% by Cuba, and 4% by Uruguay. This was because most of the migration occurred across the Atlantic before the construction of the Panama Canal. Europeans preferred to stay in countries closer to their homelands instead of taking the long trip through the Straits of Magellan or across the Andes. In 1907, European-born immigrants composed 2.4% of the Chilean population, which fell to 1.8% in 1920, and 1.5% in 1930.

After the failed liberal revolution of 1848 in the German states, a significant German immigration took place, laying the foundation for the German-Chilean community. Sponsored by the Chilean government to "civilize" and colonize the southern region, these Germans (including German-speaking Swiss, Silesians, Alsatians and Austrians) settled mainly in Valdivia, Llanquihue and Los Angeles. The Chilean Embassy in Germany estimated 150,000 to 200,000 Chileans are of German origin. 

It is estimated that nearly 5% of the Chilean population is of Asian descent, chiefly from the Middle East,  i.e., Israelis Jews, Palestinians, Syrians and Lebanese, totalling around 800,000.

Chile is home to a large population of immigrants, mostly Christian, from the Levant. Roughly 500,000 Palestinian are believed to reside in Chile, making it the home of one of the largest Palestinian communities outside of the Middle East.

Another historically significant immigrant group is Croatian. The number of their descendants today is estimated to be 380,000 persons, the equivalent of 2.4% of the population.

Over 700,000 Chileans may have British (English, Scottish or Welsh) origin, 4.5% of Chile's population. Chileans of Greek descent are estimated 90,000 to 120,000. Most of them live either in the Santiago area or in the Antofagasta area, and Chile is one of the 5 countries with the most descendants of Greeks in the world. The descendants of the Swiss reach 90,000 and it is estimated that about 5% of the Chilean populaton has some French ancestry.  184,000-800,000 (estimates) are descendants of Italians. Other groups of European descendants are found in smaller numbers.
Reference
Adapted and modified from:
https://en.wikipedia.org/wiki/Chile