I'm writing some code in PHP and want to use Apache's .htaccess to
control user access to a directory. Is there a way, after someone is
cleared into a directory with .htaccess, that I can securely retrieve
their username
from the server? I.e. I want PHP to find out what they typed to get
past the .htaccess dialog. If this isn't built into Apache, is there a
plug-in module that I can add to the server which will let it do this?

pnoeric-ga,

The username in question can be read from the $REMOTE_USER variable.
Depending on local configuration you may have to use
$_SERVER['REMOTE_USER'] instead.

Hope this helps.