Boeing's 767 model table (archived): 767-300ER first flight 12/09/86, first delivery 02/19/88, in service 03/03/88, first airline in service American Airlines; World Airline News[5]: "The first Boeing 767-300 (N351AA) was delivered to American on February 19, 1988 and entered service with AA on March 3, 1988."
American Airlines introduced the extended-range Boeing 767-300ER into service on 3 March 1988, two weeks after taking the first delivery (N351AA) on 19 February, launching what became the best-selling 767 version.