AndroidManifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android" package="App1.App1" android:versionCode="1" 
    android:versionName="1.0" android:installLocation="auto">
	<application android:label="App1" android:icon="@drawable/Icon"></application>
	<uses-permission android:name="android.permission.READ_CONTACTS" />
</manifest>

Frag.axml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical"
    android:layout_width="match_parent"
    android:layout_height="match_parent">
    <Button
        android:text="Select Contact"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:id="@+id/contactButton" />
    <TextView
        android:text="Selected Contact"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />
    <TextView
        android:id="@+id/selectedContact"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />
</LinearLayout>

Frag.cs

public class Frag : Fragment
{
    private TextView _selectedContact;

    public override View OnCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState)
    {
        var view = inflater.Inflate(Resource.Layout.Frag, container, false);

        var button = view.FindViewById<Button>(Resource.Id.contactButton);
        button.Click += (s, e) =>
        {
            var intent = new Intent(Intent.ActionPick, ContactsContract.Contacts.ContentUri);
            StartActivityForResult(intent, 9001);
        };

        _selectedContact = view.FindViewById<TextView>(Resource.Id.selectedContact);

        return view;
    }

    public override void OnActivityResult(int requestCode, int resultCode, Intent data)
    {
        if (requestCode == 9001 && resultCode == (int) Result.Ok)
        {
            if (data == null || data.Data == null)
                return;


            var addressBook = new Xamarin.Contacts.AddressBook(Activity)
            {
                PreferContactAggregation = false
            };

            var contact = addressBook.Load(data.Data.LastPathSegment);

            _selectedContact.Text = contact.FirstName;
        }
    }
}

Main.axml

<?xml version="1.0" encoding="utf-8"?>
<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:id="@+id/content"/>

MainActivity.cs

[Activity(Label = "App1", MainLauncher = true, Icon = "@drawable/icon")]
public class MainActivity : FragmentActivity
{
    protected override void OnCreate(Bundle bundle)
    {
        base.OnCreate(bundle);

        // Set our view from the "main" layout resource
        SetContentView(Resource.Layout.Main);

        SupportFragmentManager.BeginTransaction()
            .Replace(Resource.Id.content, new Frag())
            .Commit();
    }
}