The epicenter of the earthquake was about 300km (190 miles) north of the European Southern Observatory's Very Large Telescope (actually four large telescopes) on Cerro Pachon in Chile. Although the shaking there was still strong (equivalent to a magnitude 5.7 earthquake), thankfully there was little or no damage, and the telescopes returned to operation very quickly.
I've been to telescopes about 600 km (about 400 miles) further south in Chile, where the shaking was much less, but I've always been aware that earthquakes can happen there -- many of the strongest earthquakes in the world occur in Chile. It takes a lot of energy to raise the Andes mountains 15,000 feet into the sky!
Earthquakes are a fact of life when telescopes are built on mountains. Last year, telescopes on Mauna Kea were damaged by a strong earthquake there. Lick Observatory, outside of San Jose, California, has experienced several earthquakes, including the great San Francisco earthquake of 1906. Telescopes in earthquake-prone regions are engineered to withstand strong earthquakes, and a destructive earthquake (say, magnitude >7) has not yet made a direct hit on an observatory.
My best wishes go out to the citizens of northern Chile, and I sincerely hope that repairs can be made quickly.