The Neon Rain by James Lee Burke is the first novel in the Dave Robicheaux series.
This book had a publication date of March 1, 1987.
The Neon Rain book description
Detective Dave Robicheaux has fought too many battles: in Vietnam, with killers and hustlers, with police brass, and with the bottle.
Lost without his wife’s love, Robicheaux’s haunted soul mirrors the intensity and dusky mystery of New Orleans’ French Quarter – the place he calls home, and the place that nearly destroys him when he becomes involved in the case of a young prostitute whose body is found in a bayou.
Thrust into the world of drug lords and arms smugglers, Robicheaux must face down a subterranean criminal world and come to terms with his own bruised heart in order to survive.