Wash and dry the zucchini thoroughly. Using a sharp vegetable peeler or spiralizer to make “linguini noodles” with the zucchini until you reach the seeds. Discard stems and seeds.
Place the linguini in a bowl and sprinkle with salt. Let stand for half an hour so that the zucchini loses its excessive water. Gently squeeze the zucchini to drain the water.
In the mean time, season diced chicken with salt, garlic and pepper.
In a pan over medium high heat, add olive oil in and sauté chicken until golden brown.
Add halved tomatoes and zucchini. Keep stirring.
Finally, add heavy cream and Parmesan cheese in and stir well. Do not overcook this. Remove from heat, transfer to a plate and serve hot. Top with more Parmesan if desired.