A selection of human cancers harbours somatic driver mutations in genes encoding histones, most notably childhood brain tumours with K27M substitutions of the histone 3.3 gene, H3F3A. We performed whole genome sequencing of the benign cartilage tumour, chondroblastoma, and targeted sequencing of histone 3.3 genes, H3F3A and H3F3B, in seven further skeletal tumour types. We identified an exceptionally high prevalence of novel histone 3.3 driver mutations at glycine 34 and at lysine 36. Histone 3.3 gene mutations were found in 91% in giant cell tumours of bone (48/53), mainly H3F3A G34W variants, and in 92% of chondroblastoma (73/79), predominantly K36M mutations in H3F3B. H3F3B is paralogous to the cancer gene H3F3A. However, H3F3B driver variants have not previously been reported in human cancer. Our observation demonstrate remarkable tumour-specificity of mutations, with respect to which histone 3.3 gene and residue is mutated, indicating that the advantage these mutations confer is tumour dependent. Moreover, tumour-specific mutation of H3F3A and H3F3B suggests, that although both genes encode identical proteins, they are likely non-redundant and employed differentially during skeletal development.