How to allow access to an AWS Elastic Load Balancer over the DNS name

If you can guarantee that all requests will be coming from ELB (I'm not familiar with it), you could try:

real_ip_header X-Forwarded-For;
set_real_ip_from 0.0.0.0/0;

That should tell nginx to trust an X-Forwarded-For header from anyone. The downside is that if anyone directly accesses your server, they would be able to spoof an X-Forwarded-For header and nginx would use the wrong client ip address.

In the end, I implemented the requirement of our partner as follows:

• launch an instance in AWS
• allocate and attach an Elastic IP (EIP) to it
• Installed Apache
• (in our case, installed our SSL certificate)
• Configured Apache as a reverse proxy server, forwarding to a CNAME that pointed to our ELB

Here's a sample Apache virtual host configuration. I turned off NameVirtualHost and specified the address of our EIP. I also disabled a default host. If the partner desires, I will add a <Directory> block that accepts requests only from their IP range.

<IfModule mod_ssl.c>
# Catch non-SSL requests and redirect to SSL
<VirtualHost 12.34.567.890:80>
  ServerName our-static-ip-a-record.example.com
  Redirect / https://our-elb-cname.example.com       
</VirtualHost>
# Handle SSL requests on the static IP
<VirtualHost 12.34.567.890:443>
  ServerAdmin monitor@example.com
  ServerName our-static-ip-a-record.example.com

  # SSL Configuration
  SSLEngine on
  SSLProxyEngine on
  SSLProxyCACertificateFile /etc/apache2/ssl/gd_bundle.crt
  SSLCertificateFile    /etc/apache2/ssl/example.com.crt    
  SSLCertificateKeyFile /etc/apache2/ssl/private.key
  # Additional defaults, e.g. ciphers, defined in apache's ssl.conf

  # Where the magic happens
  ProxyPass / https://our-elb-cname.example.com/
  ProxyPassReverse / https://our-elb-cname.example.com/

  # Might want this on; sets X-Forwarded-For and other useful headers
  ProxyVia off

  # This came from an example I found online, handles broken connections from IE
  BrowserMatch "MSIE [2-6]" \
    nokeepalive ssl-unclean-shutdown \
    downgrade-1.0 force-response-1.0
  # MSIE 7 and newer should be able to use keepalive
  BrowserMatch "MSIE [17-9]" ssl-unclean-shutdown
</VirtualHost>
</IfModule>

Hope this saves someone else some time in the future :-)