In a large pot of boiling, salted water, cook the pasta until al dente. Drain and rinse with cold water.
In a medium saucepan, bring the shallots and oil to a simmer over medium heat and fry, stirring, until golden, 18 to 20 minutes. Using a slotted spoon, transfer to paper towels to drain; season with salt. Reserve 1/4 cup shallot oil.
In a large serving bowl, combine the chicken, cucumber, radishes, carrots, cilantro and pasta.
Whisk the lime peel and juice and honey into the reserved oil; season with salt and pepper. Drizzle over the salad, season with salt and toss. Top with the fried shallots.