The mission says the worker is on a ventilator at Los Angeles County-USC Medical Center but has shown signs of improvement. It's the first confirmed case of coronavirus on Skid Row.
About 100 people on the mission's third floor - which houses a live-in rehabilitation program and is where the employee lives - are being quarantined. Several others were sent to a quarantine facility set up at a beach RV park.
The mission's executive director said despite the positive test, they will never turn away those in need.
"I am not, and we are not, gonna let people suffer on the streets," Rev. Andy Bales said. "We will never turn our back on people who come to use. We will never lock our front door on people in need."
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The Associated Press contributed to this report.