We report on two Chandra observations, and a simultaneous Hubble Space Telescope ultraviolet observation, of the dwarf Seyfert 1 galaxy NGC 4395. Each Chandra observation had a duration of ~30 ks, with a separation of ~50 ks. The spectrum was observed to harden between these observations via a scaling down of the soft-band flux. The inter-observation variability is in a different sense to the observed variability within each observation and is most likely the result of increased absorption. Spectral variations were seen during the first observation suggesting that the X-ray emission is produced in more than one disconnected region. We have also re-analyzed a ~17 ks Chandra observation conducted in 2000. During the three Chandra observations the 2-10 keV flux is about a factor of 2 lower than seen during an XMM-Newton observation conducted in 2003. Moreover, the fractional variability amplitude exhibited during the XMM-Newton observation is significantly softer than seen during the Chandra observations. A power-spectral analysis of the first of the two new Chandra observations revealed a peak at 341s with a formal detection significance of 99%. A similar peak was seen previously in the 2000 Chandra data. However, the detection of this feature is tentative given that it was found in neither the second of our two new Chandra observations nor the XMM-Newton data, and it is much narrower than expected. The Hubble Space Telescope observation was conducted during part of the second Chandra visit. A zero-lag correlation between the ultraviolet and X-ray fluxes was detected with a significance of about 99.5%, consistent with the predictions of the two-phase model for the X-ray emission from active galactic nuclei.