Chile was important because of the nitrate mines - nitrates were required in the manufacture of explosives. Exports to Germany ceased at the beginning of WW1, which forced Germany to seek alternative supplies and resulted in her scientists discovering synthetic nitrates. By a curious twist, after the War, Germany exported those synthetic nitrates, which, it could be argued contributed to the economic decline of Chile.
The sea Battle of Coronel in November 1914 took place off the coast of Chile and in 1917, Germany's policy of 'unrestricted submarine warfare' affected every sea-faring nation directly and others indirectly (imports, travel, etc.).
Chile reacted in February 1917 by making a formal diplomatic protest, stating that the German measures were unacceptable and that Chile reserved the right to defend her ships should they be attacked by German submarines.
Source: http://www.firstworldwar.com/source/uboat_chile.htm and various other Internet sites, using Google as the search engine.