Check Radio button on div click

you can use prop() method, try the following:

$('.big').click(function() {
  $('.hli').removeClass('hli');
  $(this).addClass('hli').find('input').prop('checked', true)    
});

DEMO

please note that IDs must be unique and in order to work properly radio buttons should have name properties:

<input id="chb1" type="radio" name="radioGroup"/>
<input id="chb2" type="radio" name="radioGroup"/>

Tell me that if u want this: http://jsfiddle.net/QqVCu/6/

jQuery (Updated)

$('.big').click(function() {
    if($(this).find('input[type="radio"]').is(':checked')){
       $(this).find('input[type="radio"]').prop('checked', false);
    }
    else{
       $(this).find('input[type="radio"]').prop('checked', true);
    }
    $('.hli').toggleClass('hli');    
    $(this).toggleClass('hli');
});

How about that: http://jsfiddle.net/sgospodarets/QqVCu/5/ ? All that is necessary - wrap inputs in label. Then do not need JavaScipt.

Using a pure HTML/CSS solution:

.isHidden {
  display: none; /* hide radio buttons */
}

.label {
  display: inline-block;
  background-color: red;
  width: 120px;
  height: 120px;
  padding: 5px 10px;
}

.radio:checked + .label {   /* target next sibling (+) label */
  background-color: blue;
}

<input id="radio_1" class="radio isHidden" name="radio_a" type="radio">
<label for="radio_1" class="label">1</label>

<input id="radio_2" class="radio isHidden" name="radio_a" type="radio">
<label for="radio_2" class="label">2</label>