Mash the chickpeas using either a mortar and pestle or a large bowl with a fork. Once the chickpeas are fully mashed, mix in 1 tablespoon of the olive oil and the lime juice from 1/2 of the lime. Season with salt and pepper to taste. Set aside.
Brush a small amount of olive oil over the bread slices and toast them in the oven for 5 minutes or until lightly toasted.
Once the slices have cooled, spread 1/4 of the chickpea mixture onto each slice. Top each tartine with chives and cucumber slices. Lightly drizzle with olive oil and lime juice.
Garnish your cucumber chickpea tartine with tarragon, fresh cracked pepper and lime wedges. Enjoy!