deprecated: This repo is not updated at all anymore. Ubuntu 18.04 with nginx from the official repos now support TLS 1.3 out of the box. And that is more recommended even for experimentation.
A simple Docker container compiling Nginx from source together with Openssl from the the latest code on Github and the branch supporting TLS 1.3 draft 18.
The openssl-1.1.1-stable branch compiles with the openssl-1.1.1-stable branch from openssl
The openssl-master branch compiles with the master branch from openssl. The dev branch compiles with the tls1.3-draft-18 branch of openssl.
Size of built image: ca 210 MB
Can also be found on as pre-built image on Docker Hub as: byeskille/nginx-tls13-docker
This project is under WTFPL. So you can pretty much do whatever you want with it.
Do be warned this has had not been tested for production, and the Dockerfile is written by a person with very little knowledge about all this stuff.