sp(2)-Bonded boron nitride aerogels are synthesized from graphene aerogels via carbothermal reduction of boron oxide and simultaneous nitridation. The color and chemical composition of the original gel change dramatically, while structural features down to the nanometer scale are maintained, suggesting a direct conversion of the carbon lattice to boron nitride. Scanning and transmission electron microscopies reveal a foliated architecture of wrinkled sheets, a unique morphology among low-density, porous BN materials. The converted gels display a high degree of chemical purity (>95%) and crystalline order and exhibit unique cross-linking structures.