Cut the skin and white pith from the grapefruits. Working over a medium bowl, cut between the membranes, releasing the grapefruit segments.
Season the chicken with salt and pepper. Place the flour on a plate. In a shallow bowl, whisk the eggs and lemon juice.
In a large nonstick skillet, heat the EVOO, two turns of the pan, over medium to medium-high. Dredge the chicken in the flour, then coat in the egg mixture. Cook until the coating is golden and puffed and the chicken is cooked through, about 3 minutes per side. Transfer the chicken to a platter.
Pour the chicken stock into the skillet; cook, stirring, 2 minutes. Add the wine and cook, stirring up any browned bits, 1 minute. Melt the butter into the sauce, then stir in the tarragon, chives and grapefruit segments (but not the juice in the bowl). Pour the sauce over the chicken.