This can be done with some JavaScript, but the exact code will depend on whether or not you are using graphical radio buttons and checkboxes in your study settings. I'm going to assume you have this setting on, as is default in Lighthouse Studio.
You'll want to start by adding a copy of the Better Lighthouse Library to the same page as your free format question. You can download the question and import it into your question library from here:
https://sawtoothsoftware.com/resources/question-library/better-lighthouse-library
Then you should be able to get the behavior you're after by adding this script to your free format question:
<script>
$(document).ready(updateCheckboxes);
$(document).on('lighthouseCheckboxChanged', updateCheckboxes);
function updateCheckboxes() {
// Parameters
var variable = 'CheckVar';
// Run
var firstChecked = SSI_GetValue('[% QuestionName() %]_' + variable + '_1');
$('input[id^=[% QuestionName() %]_' + variable + '_]:not(#[% QuestionName() %]_' + variable + '_1)').each(function(){
SSI_ToggleRadioButtonOrCheckbox(this.id, firstChecked);
if (!firstChecked) {
SSI_SetSelect(this.id, false);
}
});
}
</script>
"CheckVar" should be replaced with the name of the free format variable you want this functionality to affect.