Remove Datalist Dropdown Arrow in Chrome

Thanks to Cantera. I didn't want to get rid of the black arrow entirely, just the gray square surrounding it.

input::-webkit-calendar-picker-indicator {
  background-color: inherit;
  }

Thanks to the comment by alexander farkas, here is the style rule to remove the arrow:

input::-webkit-calendar-picker-indicator {
  display: none;
}

As others have mentioned ::-webkit-calendar-picker-indicator { display: none } works at removing the arrow it would also impact the html5 datepicker on a <input type="date">,

To remove just removing the datalist input would be:

[list]::-webkit-calendar-picker-indicator { display: none; }