In a dutch oven (you want a big-ish one - 6 quart should be fine), heat olive oil on medium heat. Season chicken pieces with salt and pepper.
Cook chicken in oil 7-10 minutes, stirring occasionally, until chicken is not pink.
Remove chicken to a plate, cover with foil and keep warm.
There will probably be chicken juice and oil in your dutch oven (see picture). Discard this liquid and return the dutch oven to medium high heat.
IF, and only IF, you need to use frozen cut spinach. While the chicken is browning, put it in the microwave and cook it for 1/2 the time the bag tells you. Then let it sit 5 minutes. Then drain in a colander to get as much water out as possible.
Add the garlic to the pot and cook it for a minute or so until it's fragrant and turning light brown. If you don't have the time to mince or chop garlic they make garlic already minced or chopped in jars (as shown in the picture). I also just found garlic cloves in brine, but I haven't tried them yet.
Add Chicken Broth and Fettuccine (or whatever pasta you chose). Heat to boiling.
Reduce heat to medium and simmer uncovered for 15-25 minutes or until most of the liquid is absorbed and pasta is al dente.
While the pasta is cooking we're going to zest and juice our lemons. I picked up this tool on QVC a few years ago and it makes quick work of the zesting.
My kids somehow "lost" the glass bottoms to my juicers! But I found that I can fit them into a cereal bowl and absent another method this worked out really well.
This is what it looked like when I was done with the lemons
This what the pasta looks like when it's done simmering.
Stir 3/4 C of the grated Parmesan, the butter, lemon zest, lemon juice and your cooked chicken. Toss well to combine. Remove from heat and slowly add in spinach a handful at a time. Gently toss to incorporate. It will begin to wilt which is what you want. Let stand 5-10 minutes and serve.
If using frozen Spinach, simply add to dish and toss to incorporate. No wilting needed.
This is what our finished dish looks like with regular Fettuccine.