In a 10- to 12-inch frying pan over medium heat, toast nuts about 10 minutes; shake often.
Remove from pan; set aside.
Increase heat to medium-high.
Add oil and butter to pan; brown half the chicken at a time; this takes about 10 minutes total.
Discard fat from pan.
Return chicken and nuts to pan; add olives, 5 sage leaves, and water.
Simmer, covered, over medium-low heat until meat is no longer pink at bone (cut to test), about 25 minutes.
If made ahead, let cool, cover, and chill until next day.
Return to simmering, covered, over medium heat.
Garnish, if desired, with sage leaves.