The pace of mounted pilgrims.
Pilgrims have been travelling the Pilgrim's Way to Canterbury since before the invention of the printing press. Chaucer's Canterbury Tales is well-known to be amongst the first books printed in English, by Caxton, in the mid-15th century. Such pilgrimages were sedate affairs; it wasn't the done thing to get the pilgrimage over quickly by racing to the shrine. The 'Canterbury pace', otherwise called the 'Canterbury trot', the 'Canterbury gallop' etc. was dignified and stately.
The first time it was mentioned in print was in the Church of England clergyman William Sampson's Vow Breaker, circa 1636:
Have I practic'd my Reines [runs], my Carree'res [careers - full gallops], my Pranckers [prancings], my Ambles, my false Trotts, my smooth Ambles, and Canterbury Paces.
Pilgrims now arrive at Canterbury via the M2 motorway and the expression 'Canterbury pace' is long since forgotten. It has left us a legacy though - the word 'canter' derives directly from 'Canterbury pace'.