  We demonstrate a time scale based on a phase stable optical carrier that
accumulates an estimated time error of $48\pm94$ ps over 34 days of operation.
This all-optical time scale is formed with a cryogenic silicon cavity
exhibiting improved long-term stability and an accurate $^{87}$Sr lattice
clock. We show that this new time scale architecture outperforms existing
microwave time scales, even when they are steered to optical frequency
standards. Our analysis indicates that this time scale is capable of reaching a
stability below $1\times10^{-17}$ after a few months of averaging, making
timekeeping at the $10^{-18}$ level a realistic prospect.
