Place chicken breasts between two pieces of plastic wrap or parchment paper. Pound to an even thickness of about ¾ inch and season both sides with salt and pepper.

Whisk together honey and lime juice in a small bowl until smooth. Set aside.

Heat olive oil in a large skillet over medium-high heat. Add seasoned chicken and cook for 6-7 minutes per side, pouring glaze over chicken in the last minute.

Prepare rice according to package instructions in a separate pot. Bring water to boil, add rice, cover, and let simmer for about 15 minutes.

Slice avocados and assemble the stack: start with rice, layer with chicken, and finish with avocado slices.