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

I have an ELB. It has the address myelbname.eu-west-1.elb.amazonaws.com as one would expect.

I also have an EC2 instance behind that ELB. The load balancer is saying that the instance is healthy (the status is "In Service").

I can access the EC2 instance over IP on my network (using VPN to the VPC) but if I go to the A record of the load balancer in a browser then it can't be found.

Also, if I run nslookup it does show an IP address for the load balancer.

I've also tried adding a CNAME record and pointing it to the ELB's DNS name but that didn't work.

ELBs must be in a subnet with an internet gateway. Placing an ELB in a private subnet makes it only available within the VPC's network.