From http://pastie.org/private/cm3xnmshohsdhsiwpwq

expandingTextfield.js

var Win = Ti.UI.createWindow({
    title: "My Message",
});

var ScrollView = Ti.UI.createScrollView({
	height: Ti.UI.FILL,
	width: Ti.UI.FILL,
	contentHeight: "100%",
	contentWidth: "100%",
});

var TextArea = Ti.UI.createTextArea({
    font: {
        fontSize: 14
    },
    bottom: 40,
    width: 250,
    scrollable: false,
    backgroundColor: "#00FF00",
    height: "auto"
});

var InvisibleLabel = Ti.UI.createLabel({
    font: {
        fontSize: 14
    },
    width: 250,
    height: "auto",
    text: TextArea.value,
    visible: false
});

TextArea.addEventListener("change", function(e) {
    InvisibleLabel.text = e.value;
    TextArea.height = InvisibleLabel.height;
});

ScrollView.add(InvisibleLabel);
ScrollView.add(TextArea);
Win.add(ScrollView);
Win.open();