How to remove the blue cross on datetime-local HTML input in Chrome 27?

This is how you remove cross and arrows:

input::-webkit-outer-spin-button, /* Removes arrows */
input::-webkit-inner-spin-button, /* Removes arrows */
input::-webkit-clear-button { /* Removes blue cross */
  -webkit-appearance: none;
  margin: 0;
}

You have to use the required attribute.