Cook your pasta in well salted boiling water, undercooking by 1 minute. Reserve a cup of pasta water before draining.
Cut the chicken into bite-sized pieces and season well with salt and pepper. Lightly dust with flour and toss to coat. It helps create a nice golden crust, but is optional.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and cook for 4–5 minutes, turning the pieces until golden brown and cooked through. Remove from the pan and set aside.
In the same pan, lower the heat and gently fry the garlic in ½ tablespoon of olive oil for 1 minute. The garlic shouldn't color or burn.
Turn the heat down slightly and add the cream and pepper. Bring to a very gentle simmer, it should never boil, just a very gentle simmer.
Add the finely grated parmesan and mix it in until melted through. Let the cream slightly thicken over the heat for 1-2 minutes.
Add the cooked pasta, the lemon juice and ¼ cup of pasta water and toss continuously to thicken for a further 1-2 minutes. Add the chicken and toss gently to combine.
Take the pan off the heat and mix through the pesto, season to taste. Serve immediately with extra grated parmesan and lemon zest, if desired.