An octave-spanning coherent supercontinuum is generated by non-collinear Raman-assisted four-wave mixing in single-crystal diamond using 7.7 fs laser pulses that have been chirped to about 420 fs in duration. The use of ultrabroad bandwidth pulses as input results in substantial overlap of the generated spectrum of the anti-Stokes sidebands, creating a phase-locked supercontinuum when all the sidebands are combined to overlap in time and space. The overall bandwidth of the generated supercontinuum is sufficient to support its compression to isolated few-to-single cycle attosecond transients. The significant spectral overlap of adjacent anti-Stokes sidebands allows the utilization of straight-forward spectral interferometry to test the relative phase coherence of the anti-Stokes outputs and is demonstrated here for two adjacent pairs of sidebands. The method can subsequently be employed to set the relative phase of the sidebands for pulse compression and for the synthesis of arbitrary field transients.