Heat 2 tablespoons oil in a 10-inch heavy skillet over moderately high heat until hot but not smoking, then saute 1/2 the chestnuts with salt and pepper, to taste, stirring, until crisp on outside (being careful not to burn or cook until hard), about 4 minutes. Make other batch the same way. Remove from heat.
Halve and core pears, then cut lengthwise into thin slices.
Whisk together mustard, vinegar, and salt and pepper, to taste, in a large bowl and add remaining 6 tablespoons oil in a slow stream, whisking until emulsified. Whisk in shallot.
Add chicory, chestnuts, pears, and Stilton and toss until evenly coated. Season with salt and pepper.