Does il y a de fortes chances require the subjunctive?
No, il y a de fortes chances does not take the subjunctive:
Il y a de fortes chances que ton livre est dans ta chambre.
It is highly likely your book is in your bedroom.
À noter : There’s some disagreement about these types of expressions, but it comes down to possibility vs probability: the former requires the subjunctive, the latter the indicative. In my (and many others’) view, fortes chances is on the probability side of the scale, which calls for the indicative.