V4743 Sagittarii ( Nova Sgr 2002 No. 3) was discovered on 2002 September 20. We obtained a 5 ks ACIS-S spectrum in 2002 November and found that the nova was faint in X-rays. We then obtained a 25 ks Chandra Low Energy Transmission Grating Spectrometer (LETGS) observation on 2003 March 19. By this time, it had evolved into the supersoft X-ray phase exhibiting a continuous spectrum with deep absorption features. The light curve from the observation showed large-amplitude oscillations with a period of 1325 s ( 22 minutes) followed by a decline in the total count rate after similar to13 ks of observations. The count rate dropped from similar to 40 counts s(-1) to practically zero within similar to 6 ks and stayed low for the rest of the observation (similar to 6 ks). The spectral hardness ratio changed from maxima to minima in correlation with the oscillations and then became significantly softer during the decay. Strong H-like and He-like lines of oxygen, nitrogen, and carbon were found in absorption during the bright phase, indicating temperatures between 1 and 2 MK, but they were shifted in wavelength corresponding to a Doppler velocity of - 2400 km s(-1). The spectrum obtained after the decline in count rate showed emission lines of C vi, N vi, and N VII, suggesting that we were seeing expanding gas ejected during the outburst, probably originating from CNO-cycled material. An XMM-Newton Target of Opportunity observation, obtained on 2002 April 4 and a later LETGS observation from 2003 July 18 also showed oscillations, but with smaller amplitudes.