No, Arthur Miller's Death of a Salesman is not told chronologically. Death of a Salesman opens with the title character, Willy Loman, coming home aborting his latest sales trip.
The story then goes into a series of flashbacks from the family's history. The flashbacks focus on the successes and failures that have punctuated Willy's life, and illustrate how the failures became more common and more devastating with the passage of time. However, even these flashbacks don't occur in chronological order. Some were earlier, some were later. The flashbacks are also separated by events that are proceeding in the present time from his return home, to his final act.
The flashbacks end with Willy's most painful and disappointing failures, and blaming himself for the failures of those close to him (including his sons), and he snaps. He suddenly speeds off in his car but doesn't go far before he deliberately crashes, thus committing suicide.
The play ends with the widow and sons moving on after a scarcely attended funeral. They barely reflect on what drove the title character to suicide.