In large skillet, cook bacon over medium-high heat until crisp; drain on paper towel–lined plate. Chop and set aside. Drain all but 1 tbsp. bacon fat from skillet.
Add olive oil to skillet; sauté garlic and shallots for 2 minutes. Add Brussels sprouts; cook for 8 to 10 minutes or until tender.
Meanwhile, cook pasta according to package directions. Drain, reserving 1/3 cup cooking liquid.
Add pasta and reserved pasta liquid to pan; toss well. Stir in lemon juice and chives.