Heat the olive oil in a large heavy-bottomed pot over medium heat until shimmering, then add the diced onions. Sauté, stirring occasionally, until the onions are translucent and fragrant, about 5 minutes.
Add the chopped chicken breasts to the pot. Cook, stirring occasionally, until the chicken is lightly browned and cooked through, about 8 minutes. The chicken should be firm and no longer pink inside.
Pour in the chicken broth, then bring the mixture to a gentle simmer. Reduce the heat slightly and let it simmer, uncovered, for about 10 minutes to let the flavors meld and the chicken finish cooking.
Stir in the cream, then add a splash of lemon juice. Continue cooking gently for another 3 minutes, until the soup is heated through and slightly thickened. The soup should be smooth and velvety.
Season the soup with salt and freshly ground pepper to taste. Stir in chopped fresh herbs for brightness and aroma.
Serve the soup hot, garnished with additional herbs if desired, and enjoy the comforting yet zesty flavors in every spoonful.