Given the organization's recent troubles, the CEO job at Atlanta's Grady Memorial Hospital would appear to fall somewhere between unattractive and impossible, but industry experts said the slate of finalists is impressive. The winner will become the sixth leader of the Grady Health System in the past three years. The new head of Grady will face daunting challenges—the hospital's finance chief has projected a deficit of $18 million to $43 million this year. But all the candidates for the CEO job have dealt with some of the same problems that plague Grady, consultants say.