How to Add Choices to Existing Choice Field Using CSOM in SharePoint 2013 Online

Code Snippet 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net;
using System.Security;
using System.Text;
using System.Threading.Tasks;
using Microsoft.SharePoint.Client;

namespace CSOMOffice365
{
    class Program
    {
        static void Main(string[] args)
        {

            string userName = "[email protected]";

            Console.WriteLine("Enter your password.");
            SecureString password = GetPassword();

            // ClienContext - Get the context for the SharePoint Online Site
            // SharePoint site URL - https://c986.sharepoint.com

            using (var clientContext = new ClientContext("https://c986.sharepoint.com"))
            {

                // SharePoint Online Credentials
                clientContext.Credentials = new SharePointOnlineCredentials(userName, password);

                // Get the SharePoint web
                Web web = clientContext.Web;

                // Get the list by Title
                List list = web.Lists.GetByTitle("Custom");

                // Get a specific field by Title
                Field field = list.Fields.GetByTitle("Choice");
                FieldChoice fieldChoice = clientContext.CastTo<FieldChoice>(field);
                clientContext.Load(fieldChoice);

                // Execute the query to the server
                clientContext.ExecuteQuery();

                // Add the choice field values
                List<string> options = new List<string>(fieldChoice.Choices);
                options.Add("Option1");
                options.Add("Option2");
                options.Add("Option3");
                fieldChoice.Choices = options.ToArray();

                // Update the choice field
                fieldChoice.Update();

                // Execute the query to the server
                clientContext.ExecuteQuery();

                // Display all the choices
                foreach (string option in fieldChoice.Choices)
                {
                    Console.WriteLine(option);
                }
                Console.ReadLine();
            }

        }

        private static SecureString GetPassword()
        {
            ConsoleKeyInfo info;

            //Get the user's password as a SecureString
            SecureString securePassword = new SecureString();
            do
            {
                info = Console.ReadKey(true);
                if (info.Key != ConsoleKey.Enter)
                {
                    securePassword.AppendChar(info.KeyChar);
                }
            }
            while (info.Key != ConsoleKey.Enter);
            return securePassword;
        }
    }
}

Output