Straight from the horse's mouth
From the highest authority.
In horse racing circles tips on which horse is a likely winner circulate amongst punters. The most trusted authorities are considered to be those in closest touch with the recent form of the horse, that is, stable lads, trainers etc. The notional 'from the horse's mouth' is supposed to indicate one step better than even that inner circle, that is, the horse itself.
It is a 20th century phrase. The earliest printed version I can find of it is from the USA and clearly indicates the horse-racing context - in the Syracuse Herald, May 1913:
"I got a tip yesterday, and if it wasn't straight from the horse's mouth it was jolly well the next thing to it."