For the fondue, pour the cider into a pan and cook over a high heat until reduced by a third. Stir in the Stilton, whisking until completely melted.
In a small bowl, mix the cornflour with the cold water into a paste and stir into the cider and Stilton mixture. Stir in the fresh chives just before serving.
For the croûtes, drizzle the bread chunks with the oil and fry in a pan for 4-5 minutes, or until golden-brown and crisp.
To serve, transfer the fondue to a large serving bowl set on a large plate, arranging the croûtes around the edges of the plate.