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Soak the noodles: Boil the kettle and tip the rice noodles into a heatproof bowl. Pour over boiling water to cover. Leave noodles to soak for 4 minutes.
Whisk and toss: Meanwhile, make the dressing. Whisk together the olive oil, lemon zest and juice and mayonnaise, then season if you want to. Drain the noodles and return to the bowl. Throw in the sugar snaps, red pepper and basil. Pour in half the dressing and gently toss.
To serve: Divide the noodles between two bowls. Slice the chicken breasts and arrange on top of the noodles. Drizzle over the remaining dressing and serve.