You can use your EIP with the elastic load balancing as April has mentioned; however, when I was evaluating this it had some deficiencies that made it less than ideal for my deployment.
I have 2 Elastic IPs that are assigned to a couple of EC2 instances that serve as my front-end web servers. This are simply running threaded Apache2 servers which handle the load balancing to my application servers behind them. These two EIPs are then put in standard DNS round-robin.
The Apache2 configuration makes use of mod_balancer to balance the requests amongst the backend server instances, which is never less than 3 instances. The database runs on it's own separate EC2 instance that the backend systems can connect to.
You could replace the Apache2 configuration on my front-end systems with HAProxy. I did look at that but needed to do much more intelligent routing than I thought practical with HAProxy, but someday I may go back and re-evaluate that position.
In this configuration I'm handling over a half dozen heavily hit sites that count their hits in the tens of millions per month. The threaded front-end Apache2 servers show almost no load as they merely act as the go-between while the real work is done on the backend servers. I've noticed considerable speed performance increase from when we were running on traditional dedicated servers in co-located datacenters.