React Native - navigation issue "undefined is not an object (this.props.navigation.navigate)"

With Expo you should't do the App registration your self instead you should let Expo do it, keeping in mind that you have to export default component always: Also you need to import View and Button from react-native: please find below the full code:

import React from 'react';
import {
  AppRegistry,
  Text,
  View,
  Button
} from 'react-native';
import { StackNavigator } from 'react-navigation';

 class HomeScreen extends React.Component {
  static navigationOptions = {
    title: 'Welcome',
  };
  render() {
    const { navigate } = this.props.navigation;
    return (
      <View>
        <Text>Hello, Chat App!</Text>
        <Button
          onPress={() => navigate('Chat', { user: 'Lucy' })}
          title="Chat with Lucy"
        />
      </View>
    );
  }
}

 class ChatScreen extends React.Component {
  // Nav options can be defined as a function of the screen's props:
  static navigationOptions = ({ navigation }) => ({
    title: `Chat with ${navigation.state.params.user}`,
  });
  render() {
    // The screen's current route is passed in to `props.navigation.state`:
    const { params } = this.props.navigation.state;
    return (
      <View>
        <Text>Chat with {params.user}</Text>
      </View>
    );
  }
}

const  SimpleAppNavigator = StackNavigator({
  Home: { screen: HomeScreen },
  Chat: { screen: ChatScreen }
});

const AppNavigation = () => (
  <SimpleAppNavigator  />
);

export default class App extends React.Component {
  render() {
    return (
        <AppNavigation/>
    );
  }
}

Additional Info: When you are nesting child components, you need to pass navigation as prop in parent component. //parent.js <childcomponent navigation={this.props.navigation}/>

And you can access navigation like this

//child.js

this.props.navigation.navigate('yourcomponent');

Reference: https://reactnavigation.org/docs/en/connecting-navigation-prop.html