You will need to create two fields for this. 1) checkbox 2) text field with edit log enabled
Create a form rule that says "whenever checkbox is checked, change the text log to the value "checked" (i.e. when "myCheckbox" is checked, change "userLog" to the value in "checked"). Keep the option to fire on change only
This will create a log of entries that will give the user name and a value of "checked" each time the checkbox is checked or rechecked.
Then, if you just want the first entry, use the list function to slice by ";"
Another option would be to create a form rule that changes the text field and makes both fields uneditable once the box is checked, then the text field will only contain the name of the first person to check it.
I'm sure there are other methods, this is just off the top of my head.
