Heat oil in heavy large deep skillet (preferably nonstick) over medium-high heat. Add onion and saute until golden, about 5 minutes. Sprinkle chicken with salt and pepper. Add chicken and garlic to skillet; saute until chicken is no longer pink, about 4 minutes. Stir in rice, currants, and cinnamon sticks. Add broth and bring to boil. Reduce heat to low; cover and cook until rice is tender and most liquid is absorbed, about 20 minutes. Season with salt and pepper. Transfer to bowl. Discard cinnamon. Sprinkle with almonds.