Place chicken into a resealable plastic bag. Sprinkle with arrowroot powder and shake to coat.
Heat oil in a large skillet on medium-high heat. Add the chicken and cook for 2-3 minutes on each side until just browned and then transfer to slow cooker.
In a medium bowl, whisk together tamari through water. Pour over the chicken.
Cover the slow cooker and cook on low for 4 hours. Open the lid and add the broccoli to cook for another 20 minutes. (This can also be done during the last 4 20 minutes of the 4-hour slow cook.