Line a strainer with four layers of cheesecloth or one coffee filter and place over a bowl. Place yogurt in prepared strainer; cover yogurt with edges of cheesecloth. Refrigerate for 8 hours or overnight.
Remove yogurt from cheesecloth and discard liquid from bowl. Combine sesame seeds, salt, cayenne and cumin. Spread yogurt on a serving plate. Drizzle with oil. Sprinkle with sesame seed mixture and lemon zest. Serve with pita chips.