The Wikipedia article on Planck time says:

Theoretically, this is the smallest time measurement that will ever be possible, roughly 10^−43 seconds. Within the framework of the laws of physics as we understand them today, for times less than one Planck time apart, we can neither measure nor detect any change.

However, the article on Chronon says:

The Planck time is a theoretical lower-bound on the length of time that could exist between two connected events, but it is not a quantization of time itself since there is no requirement that the time between two events be separated by a discrete number of Planck times.

Many things in our best models of physics are discrete, but as far as I know, our coordinates (time, space, or four-dimensional space-time coordinates) are never discrete. Even something like quantum field theory, which treats things in a non-intuitively discrete way does not do this. For example, we might view the process of an electron scattering off another electron as an exchange of many discrete photons between the two electrons, but it is all written in terms of integrals or derivatives, rather than differences or sums.