Leap Seconds are a clever idea in theory, a wonderful solution when they were proposed in the 60's, but a growing nuisance in practice today. One way to avoid leap seconds is to wait until your great-great-great^N-grandchildren [1] postpone 3,600 of them and then call it a leap hour.

If you are near a cesium clock around midnight a thousand years from now, I wonder if the last second of the last minute of the first leap hour might look like this:

Notes:

1. If we assume the current earth rotation rate error of about -2 ms / day (the earth is a bit slow) and an earth deceleration rate of about -2 ms/day per century (the earth is slowing), it would take about 900 [2] years to accumulate a full hour of time error. The error is half an hour about 600 years from now.
   
2. Time error is the sum of accumulated time error due to initial frequency offset and accumulated time error due to frequency drift: TE = r T + ½ a T². Now 2 milliseconds per day frequency error is 73 seconds per century. And ½ times 2 milliseconds / day per century frequency drift squared is 36.5 seconds per century². Solving the quadratic equation, an hour of time error (3600 seconds) occurs for T = ~898 years. Of course take this value with a grain of salt since the 2 ms / day and the 2 ms / day / century frequency and frequency drift "constants" are neither exact, nor constant, nor very accurately known. But it's probably somewhere between 500 and 1,000 years. See Extrapolations of the difference (TI - UT1) for details. Similarly, earth time and atomic time will differ by half an hour ~609 years from now, around the year 2600.

You laugh, but there's an effort underway this decade to consider the idea of getting rid of leap seconds (which occur somewhat irregularly once or twice a year, or maybe every other year; except recently where we haven't had one for 5 years) and replacing them with one big leap hour sometime in the next thousand years.