Begin by heating a large nonstick skillet over medium-high heat. Pour in one tablespoon of extra-virgin olive oil and add the chicken pieces. Season the chicken with salt and pepper, cooking until they develop a golden hue on all sides, approximately 5 to 6 minutes. Transfer the chicken to a plate and set it aside.

Return the skillet to the stovetop and lower the heat to medium. Add the remaining tablespoon of olive oil and one tablespoon of butter. Introduce the garlic and shallots, sautéing them for about 3 minutes until fragrant. Sprinkle the flour over the mixture and stir it in, cooking for an additional 2 minutes to eliminate the raw flour taste.

Deglaze the pan by whisking in the white wine, allowing the liquid to reduce slightly, about 1 minute. Incorporate the lemon juice and chicken broth, continuing to whisk until the sauce is smooth. Add the capers and parsley, stirring to combine. Once the mixture begins to bubble, melt the remaining half tablespoon of butter into the sauce to enhance its sheen and richness.

Reintroduce the cooked chicken to the skillet, ensuring it is heated through, which should take 1 to 2 minutes. Toss the hot, drained pasta with the chicken and sauce, mixing thoroughly. Adjust the seasoning with additional salt and pepper if needed.

Serve immediately, garnished with freshly snipped chives for a burst of color and flavor.