Oh god, how did this get here i am not

I run a site and its main css file's pretty huge.
Looking through my server logs its being accessed the majority of times a page is reloaded.
Isn't this supposed to be stored in temporary internet history so it doesn't have to be reloaded?
Can I store it on the users computer so they only ever have to download it once?
Help me /prog/.


ExpiresActive On
<Files "*.css">
    ExpiresDefault A29030400
    Header append Cache-Control "public"
</Files>