A virtual machine (with, e.g., KVM or VirtualBox) is a better option for something like this than a
chroot or a container system like
Ubuntu 8.04 is ancient (2008) - far older than even Wheezy (2013-2016), and even wheezy is very difficult(*) to get running on a modern machine with current kernels and libc6 under
docker. It might be easier in a
chroot than a container, but I wouldn't count on it.
Installing Ubuntu 8.04 in a VM is trivially easy. Just download the installer ISO, set up a VM (e.g. with libvirt's
virt-manager GUI), and boot up the VM using the ISO.
Alternatively, it's possible to use various "physical to virtual" techniques to clone an existing machine into a VM. IMO, it's better to start with a clean, fresh install of Ubuntu 8.04, and then configure it specifically to run your ancient app.
(*) e.g. over a year ago, I had to install libc6 and a bunch of other libraries from jessie into a wheezy container just to get it running on docker. The problem was that the host running
docker had been upgraded to have libc6 2.24, and the ancient libc6 in the wheezy container did not work with that. It would have made more sense to just upgrade the container to jessie - but the app we were running in it was too old to run in jessie. so, I made a monstrous Frankenwheezy.
It sounds like your application might be a Windows 3.11 app (or maybe that was just an analogy...not sure) - with a VM, you might not even need to run Ubuntu 8.04. If that is the case, and if you have a valid license for a suitably ancient version of Windows (say, 95 or 98 or maybe XP. It's even possible to get Windows for Workgroups 3.11 itself running in KVM) then you could install that into a VM and then install your app into the VM.
If you don't have a valid license, you could try ReactOS, a Free Software clone of Windows (mostly intended to be compatible with Windows Server 2003, but might run software from earlier versions of Windows). BTW, there's a lot of crossover between ReactOS and WINE development.
Otherwise Ubuntu 8.04 + WINE would run well in a VM.