Fighting the COVID-19 pandemic, most countries have implemented non-pharmaceutical interventions like wearing masks, physical distancing, lockdown, and travel restrictions. Because of their economic and logistical effects, tracking mobility changes during quarantines is crucial in assessing their efficacy and predicting the virus spread. Chile, one of the worst-hit countries in the world, unlike many other countries, implemented quarantines at a more localized level, shutting down small administrative zones, rather than the whole country or large regions. Given the non-obvious effects of these localized quarantines, tracking mobility becomes even more critical in Chile. To assess the impact on human mobility of the localized quarantines in Chile, we use a mobile phone dataset made available by Telefónica Chile, which comprises 31 billion eXtended Detail Records and 5.4 million users covering the period February 26th to September 20th, 2020. From these records, we derive three epidemiologically relevant metrics describing the mobility within and between comunas. The datasets made available can be used to fight the COVID-19 epidemics, particularly for localized quarantines' less understood effect.