Identical triplets are rare, but not unheard of. Sam Orbaum, who wrote for the Jerusalem Post (before he died of cancer a few years ago) daughters are identical triplets.
Identical triplets could either be surviving quadruplets (the embryo split 4 ways) or be a second split from one of the embryos (identical twins, one of which split again).
Apparently identical twins as part of a set of triplets are more common than most people think. Of naturally born triplets (i.e. not a result of using fertility drugs) many are "a pair and a spare" - in reasearch done by Triplet Connection in 1988 (quoted in Elizabeth Noble's book - Having Twins), 6% of the triplets were monozygotic (all identical); 28% trizygotic (all fraternal); and 66% singleton plus monozygotic, with a boy & 2 girls being the most likely combination.
