'Chips: A Free (and Easy) School' is solely by Dickens.
The paper referred to below, 'A Free (and Easy) School,' by Dickens and Henry Morley, appeared in Household Words on 15 November 1851 (see p. 169).
According to Morley, the 'Chip' owed its origin to a strange coincidence. The master of the school turned out to be one of Dickens' old tailors. Morley describes what happened:

Poor Mr. C. [the tailor-schoolmaster] has been several times to Dickens, having been, utterly to my surprise, almost 'snuffed out by an article.' Trustees had been down upon him, and parents were writing to remove their sons. A note from Dickens, with this paragraph ['Chips: A Free (and Easy) School'], have set him right again - as nobody could wish to do him injury. The poor fellow appealed simply for pity - said every word was true, and was, said Dickens, 'quite awe-struck at the cleverness of the young man.' ...
Dickens imitated him, not mockingly - but you know his talent for mimicry - and he expressed quite touchingly the poor fellow's appeal, to which, of course, he had responded generously [Solly, The Life of Henry Morley, p.198].

Six years later, when Morley reprinted 'A Free (and Easy) School' in Gossip he completely changed the physical description of the schoolmaster and completely altered the exterior of the school.

Harry Stone; © Bloomington and Indiana University Press, 1968. DJO gratefully acknowledges permission to reproduce this material.