When they met, Margaret Oliver was a wheelchair-bound 93-year-old living at the Jewish Home & Hospital on Manhattan’s Upper West Side, and Elvis Checho was a 20-year-old volunteer, an impoverished immigrant from the Dominican Republic. Not much had gone right in Elvis’ life until the two struck up their unlikely but very real friendship. ”If I had never met you, I’d probably be dead or in jail,” he once told her. Sonny Kleinfield, a New York Times writer, had wonderful access for His Oldest Friend, and it shows: Ms. Oliver and Elvis only grow closer as she becomes older and frailer, her eyesight failing, and as he struggles with rent, chronic back pain, college, and fatherhood. This is a spare, moving account that never cloys or sticks.