Heat oil over medium heat in a large non-stick skillet. Add apples, onion, and jalapeno, saute until golden and tender about 15 minutes. Stir in currants, brown sugar and all spice. Pour in Tree Top juice and vinegar; continue cooking until all liquid is absorbed. Set aside to cool.
Place 4 tortillas onto work surface, divide each with chicken, cheddar cheese and blue cheese. Top with remaining tortillas.
In a large non-stick skillet heat 1 teaspoon oil over medium-high heat. Working in batches cook quesadillas one at a time until golden on both sides adding more oil if needed. Keep cooked quesadillas warm in 250F. oven on large baking sheet until finished.
Cut quesadillas into wedges and top with prepared apple chutney.