Create a Checklist Custom Field
In order to use a new checklist field, create a new custom field on JIRA. This option is found on Administration area, under Custom Fields side menu.
Click Add Custom Field button and select the Advanced left menu as shown below. There, the checklist custom field type is available to be chosen.
Once the custom field type has been chosen as Checklist, just follow the default JIRA wizard to finish the custom field creation.