Build and Runes
Try not to get yourself isolated, as he deals increased damage to isolated targets.
Kha’Zix’s jump ability has a long cooldown, so if he wastes it then punish him hard for it.
Kha’Zix’s Leap is a strong gap closer, especially when evolved. Try to pick champions that can CC him (e.g. Kennen, Fiddlesticks, Renekton) or disengage from him (e.g. Ezreal, Vladimir, LeBlanc) when Kha’Zix uses his Leap.
Kha’Zix is an epitomal assassin; near-instantaneous kills on isolated targets but dependant on surprise attacks. Build defensively and scry the entire map with wards and trinkets.