Place ham bone, split peas, celery, carrots, onion, salt, thyme, bay leaf, and pepper into a large pot; pour in water. Bring mixture to a boil and skim off any foam with a spoon.
Reduce the heat and place a lid on the pot, slightly ajar to allow some evaporation. Simmer, stirring occasionally, until peas are tender and soup is thick, about 3 hours.
Remove ham bone from soup; remove meat from ham bone, chop, and return to the pot.