We present time-resolved optical spectroscopy of V458 Vulpeculae (Nova Vul 2007 No. 1) spread over a period of 15 months starting 301d after its discovery. Our data reveal radial-velocity variations in the HeII λ5412 and HeII λ4686 emission lines. A period analysis of the radial-velocity curves resulted in a period of 98.09647 +/- 0.00025min (0.06812255 +/- 0.00000017d) which we identify with the orbital period of the binary system. V458 Vul is therefore the planetary nebula central binary star with the shortest period known. We explore the possibility of the system being composed of a relatively massive white dwarf (M1 >~ 1.0 Msolar) accreting matter from a post-asymptotic giant branch star which produced the planetary nebula observed. In this scenario, the central binary system therefore underwent two common-envelope episodes. A combination of previous photoionization modelling of the nebular spectra, post-asymptotic giant branch evolutionary tracks and the orbital period favour a mass of M2 ~ 0.6 Msolar for the donor star. Therefore, the total mass of the system may exceed the Chandrasekhar mass, which makes V458 Vul a Type Ia supernova progenitor candidate.