Undefined is not a object in this.state - ReactNative

You need to bind this to the function addRow like this:

<TouchableHighlight onPress={ this.addRow.bind(this) } >
  <Text>Add</Text>
</TouchableHighlight>

or create an anonymous function to automatically bind this:

<TouchableHighlight onPress={ () => this.addRow() } >
  <Text>Add</Text>
</TouchableHighlight>

For explanation refer to this.