The hosts had the better of the first half chances. Fabio Saraiva fluffed his lines after a poor pass from Hornets skipper Jack Brivio, before Gus Sow rattled the woodwork with a rasping drive.
Horsham’s best opportunity of the half came on the stroke of half-time. Shamir Fenelon’s deflected effort went just wide after excellent work from Brivio.
Chances were few and far between in the second half. Kadell Daniel’s fierce drive was deflected wide in a rare Hornets attack, while Dan Hector flashed a shot narrowly wide for Leatherhead at the death.
The two sides will meet again in a replay at the Camping World Community Stadium on Tuesday evening (7.45pm).
See some pictures by the club's photographer John Lines on this page and the ones linked.
Get the latest from the Camping World Community Stadium in the West Sussex County Times - out every Thursday.
1. Leatherhead 0, Horsham FC 0 - the match in pictures
FA Cup first qualifying round action between Leatherhead and Horsham FC Photo: John Lines
2. Leatherhead 0, Horsham FC 0 - the match in pictures
FA Cup first qualifying round action between Leatherhead and Horsham FC Photo: John Lines
3. Leatherhead 0, Horsham FC 0 - the match in pictures
FA Cup first qualifying round action between Leatherhead and Horsham FC Photo: John Lines
4. Leatherhead 0, Horsham FC 0 - the match in pictures
FA Cup first qualifying round action between Leatherhead and Horsham FC Photo: John Lines