I tracked the issue.
local_transport = local
content_filter = smtp-amavis:[127.0.0.1]:10024
header_checks = pcre:/etc/postfix/pcre-header.cf
body_checks = pcre:/etc/postfix/pcre-body.cf
biff = no
#transport_maps = hash:/etc/postfix/transport
The parameters local_transport and transport_maps conflicted. As soon as I commented out transport_maps, I started getting mail.
This might have to to with the fact that I'm running virtual mail domains. I dunno.