Although Other Answers work well, i want to give you alternate short version which i use very often:
Customer::select('customers.*')
->leftJoin('orders', 'customers.id', '=', 'orders.customer_id')
->whereNull('orders.customer_id')->first();
And as in laravel version 5.3
added one more feature which will make your work even simpler look below for example:
Customer::doesntHave('orders')->get();