The full code needed to create a bot framework bot and host on Azure Functions

CompleteAzureFunctionBotFrameworkBot.cs

[FunctionName("ChatFunction")]
public static async Task<HttpResponseMessage> ChatFunction([HttpTrigger(AuthorizationLevel.Anonymous, Route = "v1/messages")] HttpRequestMessage req,
                                                                   TraceWriter log)
{
	using (BotService.Initialize())
	{
		// authenticate incoming request and add activity.ServiceUrl to MicrosoftAppCredentials.TrustedHostNames
		// if request is authenticated
		if (!await BotService.Authenticator.TryAuthenticateAsync(req, new[]
		{
			activity
		},CancellationToken.None))
		{
			return BotAuthenticator.GenerateUnauthorizedResponse(req);
		}

		// Deserialize the incoming activity
		string jsonContent = await req.Content.ReadAsStringAsync();
		var activity = JsonConvert.DeserializeObject<Activity>(jsonContent);

		if (activity != null)
		{
			if (activity.Type == ActivityTypes.Message)
				await Conversation.SendAsync(activity,() => 
																			new NewPostcardDialog(Conversation.Container.Resolve<IAppSettingsService>(),
																														Conversation.Container.Resolve<IPaypalService>(),
																														Conversation.Container.Resolve<ITableService>(),
																														Conversation.Container.Resolve<IBugTrackingService>(),
																														Conversation.Container.Resolve<IAnalyticsService>()));
		}
		return new HttpResponseMessage(HttpStatusCode.OK);
}