Place the potatoes on the bottom of a 4- to 6-quart slow cooker. Add the chicken, leeks, wine, and 1 teaspoon salt.
Cook, covered, until the chicken and potatoes are tender, on high for 3 to 4 hours, or on low for 6 to 7 hours.
Transfer the chicken and all but 4 of the potatoes to plates. Using a fork, smash the remaining potatoes into the cooking liquid to thicken.
Add the peas and cream and cook just until heated through, 3 to 5 minutes. Spoon over the chicken and sprinkle with the tarragon.