HTMLSelectElement.disabled

aSelectElement.disabled = aBool;

<label>
  Allow drinks?
  <input id="allow-drinks" type="checkbox"/>
</label>

<label for="drink-select">Drink selection:</label>
<select id="drink-select" disabled>
  <option value="1">Water</option>
  <option value="2">Beer</option>
  <option value="3">Pepsi</option>
  <option value="4">Whisky</option>
</select>

var allowDrinksCheckbox = document.getElementById("allow-drinks");
var drinkSelect = document.getElementById("drink-select");

allowDrinksCheckbox.addEventListener("change", function(event) {
  if (event.target.checked) {
    drinkSelect.disabled = false;
  } else {
    drinkSelect.disabled = true;
  }
}, false);