Season the chicken with salt and pepper. Add the olive oil to the skillet, throw in the chicken and brown on all sides, 4 to 5 minutes. Remove and reserve.
Add the onions, zucchini and squash and cook, stirring occasionally, for 2 to 3 minutes. Move those vegetables to the edges of the skillet and add the kale, tomatoes, corn and garlic. Cook, stirring occasionally, until the kale turns bright green, an additional, 1 to 2 minutes.
In a small bowl, stir together the pesto and cream.
Return the chicken to the skillet along with any juices. Add the pesto cream and reduce the heat to medium. Cook, stirring, for an additional 1 to 2 minutes. Remove from the heat and stir in the lemon juice and grated Parmesan. Enjoy.