Whisk the flour and salt together in a large mixing bowl, then stir in the olive oil until the mixture looks like coarse crumbs.
Gradually add the water while mixing until a firm dough forms, adding a splash more water only if the flour is not fully incorporated.
Cover the bowl with a damp kitchen towel and let the dough rest at room temperature for at least 45 minutes to relax the gluten.
Divide the dough into 6 equal portions and roll each into a smooth ball.
Roll each ball out into a thin circle on a lightly floured surface, then cut each circle in half to create two semi-circles.
Lightly dampen the straight edge of a semi-circle with water, fold it into a cone shape, and pinch the seam firmly to seal.
Fill each cone with a portion of the shredded chicken, then dampen the top edges and press them together to seal the samosa completely.
Heat a few inches of oil in a deep pot to medium-high heat.
Fry the samosas in batches until they are deep golden brown and crispy, turning them occasionally to ensure even cooking.
Transfer the finished samosas to a paper towel-lined plate to drain before serving.