Trim chicken thighs of any excess fat. Place them in the slow cooker bowl and scatter garlic cloves over top.
In a small bowl, stir together the lemon zest, juice and the chicken broth; pour half of it (about 1/3 cup) into slow cooker. Cover and cook for 3 hours on HIGH or 5 hours on LOW.
Remove chicken thighs to a platter and keep warm; discard garlic cloves. In a small bowl, stir together remaining 1/3 cup lemon juice mixture, cornstarch, salt and pepper. Whisk into slow cooker bowl with chopped spinach and cook another 30 minutes on HIGH or LOW.
Meanwhile, cook pasta according to package directions, about 4 minutes. Stir half of sauce from slow cooker bowl into pasta and serve remainder with chicken.
