In the Instant Pot®, add chicken and tomatoes. Lock lid.
Press the Manual or Pressure Cook button and adjust time to 5 minutes. When timer beeps, let pressure release naturally for 10 minutes. Quick-release any additional pressure until float valve drops. Unlock lid. Check chicken using a meat thermometer to ensure internal temperature is at least 165°F.
Using a slotted spoon, transfer chicken and tomatoes to four bowls. Season with salt and pepper. Add mozzarella halves. Drizzle with oil and balsamic vinegar. Garnish with basil. Serve immediately.