No, Chelsea are very much in debt. It's just that Abramovich has the financial muscle to stop it spiralling out of control.
No Chelsea are not in debt. They made massive losses last year, but it's quite different to debt. Their profit and loss acount was negative at the end of the year which simply means more money went out than in (ie, they spent more than they received). This is hardly suprising given the amount they spent on buying players, of course they spent more than the revenue they received. Debt would be owing someone something, like a bank loan or whatever (ie, what we have with the new stadium an all), and as far as I know Chelsea are certainly not "very much in debt." Just simply made a loss rather than a profit for the financial year, which is not worrying in the slightest.