Chapman's first work was The Objection of a late anonymous writeragainst the Book of Daniel considered, Camb. 1728. This was followed by Remarks on Dr. Middleton's celebrated Letter to Dr. Waterland, Lond. 1738, of which later editions appeared. He next published Eusebius, or the True Christian's Defence, directed against Thomas Morgan's Moral Philosopher, and Matthew Tindal's Christianity as old as the Creation, in 2 vols. Lond.. William Warburton, in a letter to Philip Doddridge, criticised its slips, and said "it was written by order of the A. B. C.". In his essay De Ætate Ciceronis Libr. de Legibus, Camb. 1741, addressed to James Tunstall, and published with his Latin epistle to Conyers Middleton, Chapman proved for the first time that Cicero had published two editions of his Academica. In 1744 his letter On the ancient numeral characters of the Roman Legions, was added to Tunstall's Observations on Epistles of Cicero and Brutus, Lond., in confutation of Middleton's notion that there were legions of the same number in different parts of the empire. In 1742 he published Miscellaneous Tracts relating to Antiquity, in five parts, Lond. In 1745 he assisted Zachary Pearce in his edition of Cicero de Officiis. In 1747 he prefixed anonymously in Latin to Richard Mounteney's edition of Demosthenes his Observationes in Commentarios vulgò Ulpianeos, and a map of ancient Greece. Editions of this work appeared in 1791, 1811, and 1820. His other works were:
Charge to the Clergy of the Archdeaconry.... Popery the true Bane of Letters, Lond. 1746, which was attacked by Middleton;
The Jesuit Cabal further opened, Lond. 1747;
Discovery of the Miraculous Powers of the Christian Church, Lond. 1747;
Concio ad Synodum.... Prov. Cant., Lond. 1748;
Ends and Uses of Charity Schools, Lond. 1752; and
Miraculous Powers of Primitive Christians, Lond. 1752; also
single sermons in 1739, 1743, 1748, and 1752.
Legal case
As executor and surviving trustee of Archbishop Potter, Chapman presented himself to the precentorship of Lincoln. A suit was then brought in chancery by William Richardson. In 1760 Lord-keeper Henley made a decree in his favour, but the House of Lords reversed the decision. Richard Burn stated the case in Ecclesiastical Law, vol. i., but promised Chapman to modify the statement in a later edition. Richard Hurd censured Chapman in his correspondence with Warburton; and Chapman published his own statement, ‘His Case against Dr. Richardson,’ &c., Lond. 1760, which was not answered.