Instead of only the little tiny down arrow? Seems like there should be a property I can set or something, but I'm not seeing one... unless I'm blind.
Are you looking for
comboBox1.DropDownStyle = ComboBoxStyle.DropDownList;
maybe? That will make the combo box non-editable, i.e. it won't act like a text box with a button but just as a large button that will open the drop-down.