The 27-year-old shooter developed a condition where the veins of the patient have blood clots which results in trouble in breathing.
It came as a setback but National Rifle Association of India secretary Rajiv Bhatia said there was nothing to worry about and he is being getting ready to be discharged.
"He was not keeping well as he had pneumonia, but he is ok now, and will be discharged today. He will also resume his training," Bhatia said.
Chain Singh is scheduled to participate in 50m rifle prone and 50m rifle 3 positions at the Games.
He will be flying out to Rio on August 1.
Chain Singh won a bronze medal at the 2014 Incheon Asian Games in 50m rifle 3 positions.
