How/Where to store data in a Chrome Tampermonkey script?
Since you are using Tampermonkey (Chrome) and Greasemonkey (Firefox). Go ahead and use GM_setValue(). It cannot be cleared by Facebook or by any other website.
It has the advantage of storing values cross-domain, as well.
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Beware that the bog-standard GM_setValue() is somewhat problematic on Firefox. It can cause a script instance to crash on invalid values -- So it's best to use a serializer, such as GM_SuperValue, to store anything but strings. Even innocent-looking integers can cause the default GM_setValue() to crash.
Currently, only GM_setValue(), cookies, localStorage, and IndexedDB are available for persistent data on both browsers.
IndexedDB would also probably do what you want, but it is nowhere as easy to use as GM_setValue().
Update:
Nowadays, don't forget to use:
// @grant GM_setValue
and// @grant GM_getValue
Also, if you do use the GM_SuperValue library, you would now add it with:
// @require http://userscripts-mirror.org/scripts/source/107941.user.js in the metadata block. (Since userscripts.org is long dead.)