In a saucepan over medium heat, combine the oil and shallot and cook until the shallot rings are translucent, about 5 minutes.
Add the pineapple and sugar and cook, stirring to coat the pineapple with the sugar, until the sugar is dissolved and the pineapple begins to soften.
Add 1/4 cup of the pineapple juice and the balsamic vinegar and cook until the liquid is reduced by half, about 5 to 7 minutes.
Add the remaining juice and cranberries and cook until the cranberries pop and the juice thickens, about 3 to 5 minutes.
Stir in the thyme and serve. The chutney will keep, tightly covered, in the refrigerator up to one week.