You can do this using client side validations on your form. The idea is that you apply the required validations on the checkbox and as a response to that validation you use the show/hide layer response. In this show hide response you select the triggering form element, the checkbox, then the target for element, your text field for that checkbox. You then specify 'if trigger is valid' then 'show target layer'.
I'm including an example of this on a page so that you have a reference.