Bring a pot of water to a boil and cook the udon noodles according to package instructions, then drain and set aside.
In a small bowl, whisk together the creamy peanut butter, tamari, lime juice, grated fresh ginger, and sriracha until smooth.
Slice the chicken breast into bite-sized strips and season with sea salt and black pepper.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and sauté for 5-6 minutes until golden and cooked through.
Add the minced garlic, sliced red bell pepper, and snap peas to the skillet, stir-frying for 3 minutes until the vegetables are tender-crisp.
Add the cooked udon noodles and the peanut sauce to the skillet.
Toss everything together for 1-2 minutes until the noodles are well-coated and the sauce has thickened slightly.
Serve immediately, garnished with an extra squeeze of lime if desired.