I remember watching this on late night TV during the late 80s/early 90s (I think). The theme song was 'Paint It Black'. I seem to remember that Rosalind Chao was in one episode (Keiko O'Brien in Star Trek).

Lordy folks...this show ran on CBS from 1987 thru 1990.  Season 2 ran specifically in 1989, from Jan. to May.  Season 1 ran Sept. '87 thru April '88 and Season 3, probably Sept. '89 thru April '90.

Tour of Duty was about a platoon in Vietnam from 1967-1969.  It basically followed real-world events in the Vietnam TOO.  The 2nd Season opens up with a 2-parter called Saigon which deals with the Tet Offensive.  Season 1 ends with clues to the beginning of Tet.   So the continuity is pretty good.

Season 1 had actor Kevin Conway, (yes, that Kevin Conway), the Batman himself.  He played the captain of the platoon that gets killed about 5 episodes or so from the end of Season 1.

Oh yeah...this series isn't shy about killing off main characters.  Several main characters get knocked off in the first season.  At least three that I can think of.