Put chicken, leek, garlic, broth, chicken salt and pepper in a 4-quart slow cooker. Cover and cook on low for 6 hours until the thighs are tender and at least 165°F.
Lift chicken to a plate and shred into large pieces. Stir cream and cream cheese into the hot cooking liquid, cover and cook on high for 15 minutes, stirring once until smooth.
Meanwhile, cook rotini in water with the tablespoon salt until just tender. Reserve 1 cup pasta water before draining.
Turn the slow cooker off and stir Parmesan into the sauce gradually. Fold in shredded chicken and cooked pasta.
Loosen with reserved pasta water a few tablespoons at a time only if needed, then serve promptly while the sauce coats the rotini.