We present quasi-simultaneous ASCA and RXTE observations of the most luminous known AGN in the local (z<0.3) Universe, the recently discovered quasar PDS 456. Multiwavelength observations have been conducted which show that PDS 456 has a bolometric luminosity of 10^47 erg/s peaking in the UV part of the spectrum. In the X-ray band the 2-10 keV (rest-frame) luminosity is 10^45 erg/s. The broad-band X-ray spectrum obtained with ASCA and RXTE contains considerable complexity. The most striking feature observed is a very deep, ionised iron K edge, observed at 8.7 keV in the quasar rest-frame. We find that these features are consistent with reprocessing from highly ionised matter, probably the inner accretion disk. PDS 456 appeared to show a strong (factor of 2.1) outburst in just 17ksec, although non-intrinsic sources cannot be completely ruled out. If confirmed, this would be an unusual event for such a high-luminosity source, with the light-crossing-time corresponding to 2 Schwarzschild radii. The implication would be that flaring occurs within the very central regions, or else that PDS 456 is a `super-Eddington or relativistically beamed system. Overall we conclude on the basis of the extreme blue/UV luminosity, the rapid X-ray variability and from the imprint of highly ionised material on the X-ray spectrum, that PDS 456 is a quasar with an unusually high accretion rate.