Cook your pasta in well salted boiling water, undercooking by 1 minute. Reserve a cup of pasta water before draining.
Flatten the chicken breast to an even thickness (about 1-1.5cm), I do this by laying some plastic wrap over the top and hitting with a rolling pin. If your breast is quite thick then you can cut into bite size pieces and pan fry like that.
Season the breast well with salt and pepper on each side then dust with the flour.
Heat 1 tbsp of olive oil in a fry pan over a medium high heat and fry the chicken for 2 mins each side (or until cooked through if yours is thicker). You can also pan fry in bite size pieces.
Lightly wrap in foil and set aside.
In a large skillet that will fit all the pasta at end, heat 1 tbsp of olive oil over medium heat and fry the garlic for 1 - 2 minutes, a gentle sizzle. The garlic shouldn't color or burn.
Turn the heat down slightly and add the cream. Bring to a very gentle simmer, it should never boil, just a very gentle simmer.
Add the lemon juice and pepper and whisk in quickly.
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 pesto, mix through then add your cooked pasta and toss. Let it very gently bubble away for 1 - 2 minutes. Season to taste.
Add a splash of pasta water if you need to loosen. Cream sauces thicken up really quickly off the heat so you want it on the saucier side in the pan.
Divide between bowls, slice your chicken and place on top with some extra grated parmesan if you wish and I love to top with some grated lemon zest and a couple of basil leaves.