Place the dates in a small bowl and cover them with boiling water. Allow them to stand for 5 minutes so they will get plump.
Meanwhile, heat a small nonstick pan over medium-high heat. Add the almonds and stir until toasted, just a few minutes, then remove from heat and set aside.
Place the chicken breasts on a cutting board, smooth side down. Cover with plastic wrap and pound the meat to ¼-inch thickness. Season with salt and pepper, then set aside.
Preheat the oven to 375°F.
Drain the water from dates, then combine with the goat cheese, almonds, and thyme. Mix well.
Add ¼ of the goat cheese mixture to each chicken breast. Spread it evenly across the breast, but don’t go all the way to the edges.
Starting at the narrow end, roll the chicken breasts up and secure each one with kitchen twine or wooden toothpicks.
Heat olive oil in an ovenproof skillet over medium heat.
Add the chicken rolls and cook for about 5 minutes total until they’re browned on all sides but not cooked.
Place the chicken pieces seam-side down on a baking tray lined with parchment paper. Set the tray in the oven and bake for 15 minutes or so until the chicken is cooked through.
Combine the honey and lemon juice in a small bowl. Brush the mixture over the chicken and bake an additional 2 to 3 minutes.
Remove the twine or toothpicks, slice into rolls, and serve immediately.