If you are using your own Chef cookbooks you certainly have some sort of tests for them. Likely running test-kitchen with docker or vagrant driver. That setup works perfectly fine locally or on a self-hosted Jenkins server. However building them on public CI platforms like travis-ci or drone.io is not possible like that. Caused by their virtualization technology, we cant use test-kitchen with docker or vagrant driver there.
What people usually do to solve this: Use a cloud driver like EC2, Cloudstack, Rackspace so travis-ci will spin up a VM there. However I found this very clunky. This require additional accounts and costs with a Cloud provider.
So what I did is mimicing how the chef-zero provisioner for test-kitchen works as seen here https://github.com/test-kitchen/test-kitchen/blob/master/lib/kitchen/provisioner/chef_zero.rb
It basically boils down to installing Chef, copying all dependency cookbooks in place along with some configs and then running chef-client with chef-zero.