How can I create a check list that has a drop down.

For example I want to have a lit of skills and have the user then provide a skill level for each skill.  For example if I'm do Drywall I want to be able to check that option and then provide a skill level of DIY, Past Trade Experience, Current Trade Experience, Licensed. 

You can achieve this by adding separate checkbox and option for each skill and skill level. 

You can also try to use the Input Table field instead of a checkbox and drop-down field. Here is a sample setup of the Input Table based on your requirements.