Pour the chicken broth into an Instant Pot or other multi-cooker and set to sauté. Add the thyme, ham and butter. While the broth heats, chop the celery, cut the carrots into 1/2-inch-thick rounds, halve the leek lengthwise and thinly slice and chop the garlic; add the vegetables to the pot as you cut them.
Rinse the split peas in a colander, discarding any small stones, then add to the pot. Secure the lid, making sure the steam valve is in the sealing position, and set the cooker to high pressure for 15 minutes. When the time is up, carefully turn the steam valve to the venting position to release the pressure.
Turn off the cooker. Remove the lid and stir the soup; discard the thyme sprigs. Thin the soup with up to 1 cup water if needed (the soup will continue to thicken as it cools). Season with salt and pepper. Divide among bowls and top with the pita chips.
Photograph by Ryan Dausch