Place the chicken thighs in the bottom of the slow cooker. Add the cubed sweet potatoes and diced onion on top.
In a small bowl, stir together the minced garlic, grated ginger, red curry paste, coconut milk, chicken broth, and fish sauce until smooth. Pour this mixture over the chicken and vegetables.
Cover the slow cooker and cook on low for 6 to 7 hours, until the chicken is tender and the sweet potatoes are soft.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the pot and stir to combine with the sauce.
Stir in the lime juice right before serving. Ladle the curry into bowls and top each portion with chopped cilantro.