Rinse apricots and scatter them in a slow cooker. Pat chicken dry; season with salt and pepper. Melt butter in oil in a large skillet over medium-high heat. Cook thighs until golden brown, 3 to 5 minutes per side. (Brown in batches to avoid crowding skillet.) Arrange over apricots.
Pour off all but 1 Tbsp. fat in skillet. Add onion and cook until just soft, 2 to 4 minutes.
Add broth to skillet; turn heat to high. Bring to a boil, loosening browned bits.
Pour contents of skillet over apricots and chicken. Cover and cook on low heat for 4 hours.
Carefully transfer thighs to a serving dish (they'll tend to fall apart easily); cover with foil to keep warm. Pour remaining contents into a saucepan. Boil, stirring often, until reduced and thickened, about 10 minutes. Pour over chicken.
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