import flash.text.TextFormat;
import fl.controls.TextArea;
import flash.events.Event;

var myTextArea:TextArea = new TextArea();
myTextArea.setSize(200, 100);
myTextArea.text = "Hello World";

var myTextFormat:TextFormat = new TextFormat();
myTextFormat.font = "Arial";
myTextFormat.size = 22;
myTextFormat.bold = false;
myTextFormat.italic = false;
myTextFormat.underline = false;
myTextArea.setStyle("textFormat", myTextFormat);

myTextArea.x = 30;
myTextArea.y = 30;
addChild(myTextArea);

myTextArea.setStyle("focusRectSkin",Sprite);

myTextArea.addEventListener(Event.CHANGE, onMyTextArea_CHANGE);

function onMyTextArea_CHANGE(event:Event)
{
    myTextArea.text = myTextArea.text.replace("\r", "");
}

http://stackoverflow.com/questions/1239891/as3-textarea-component-disallow-user-to-enter-a-line-break

There is no built-in way of preventing the user pressing the Enter Key in a TextArea Component (in a standard TextField you can set multiline = false). Instead, you need to listen for the CHANGE event and then remove the Carriage Retun (\r) character.

AS3 Prevent Multiline in TextArea Component

ActionScript 3