From Blackstone, year 1765: http://press-pubs.uchicago.edu/founders/documents/a1_8_4_citizenships1.html
Yet the children of the king's embassadors born abroad were always held to be natural subjects: for as the father, though in a foreign country, owes not even a local allegiance to the prince to whom he is sent; so, with regard to the son also, he was held (by a kind of postliminium) to be born under the king of England's allegiance, represented by his father, the embassador. To encourage also foreign commerce, it was enacted by statute 25 Edw. III. st. 2. that all children born abroad, provided both their parents were at the time of the birth in allegiance to the king, and the mother had passed the seas by her husband's consent, might inherit as if born in England: and accordingly it hath been so adjudged in behalf of merchants. But by several more modern statutes these restrictions are still farther taken off: so that all children, born out of the king's ligeance, whose fathers were natural-born subjects, are now natural-born subjects themselves, to all intents and purposes, without any exception; unless their said fathers were attainted, or banished beyond sea, for high treason; or were then in the service of a prince at enmity with Great Britain.
From various members of the 1st Congress debating the 1790 Naturalization Act. (Note Jackson's use of Blackstone, and the other's use of British law.):
Mr. Jackson.--It was observed yesterday, Mr. Chairman, that we could not modify or confine our terms of naturalization; that we could not admit an alien to the rights of citizenship progressively. I shall take the liberty of supporting the contrary doctrine, which I contend for, by the reference to the very accurate commentator on the laws of England, Justice Blackstone, I, 10.--"Naturalization," says he, "cannot be performed but by an act of Parliament; for by this an alien is put in exactly the same state as if he had been born in the King's legiance, except only, that he is incapable, as well as a denizen, of being a member of the Privy Council, or Parliament, holding offices, grants, &c. No bill for naturalization can be received in either House of Parliament without such disabling clause in it." So that here we find, in that nation from which we derive most of our ideas on this subject, not only that citizens are made progressively, but that such a mode is absolutely necessary to be pursued in every act of Parliament for the naturalization of foreigners. Representative James Jackson, Georgia, Officer during Revolution in State Militia, delegate to provincial Congress and to State Convention.
Mr. Burke....The case of the children of American parents born abroad ought to be provided for, as was done in the case of English parents, in the 12th year of William III. There are several other cases that ought to be likewise attended to.Aedanus Burke, South Carolina, who had been an officer in the Continental Army.
Mr. Hartley observed, that the subject was entirely new, and that the committee had no positive mode to enable them to decide; the practice of England, and the regulations of the several States, threw some light on the subject, but not sufficient to enable them to discover what plan of naturalization would be acceptable under a Government like this. Some gentlemen had objected to the bill, without attending to all its parts, for a remedy was therein provided for some of the inconveniences that have been suggested. It was said, the bill ought to extend to the exclusion of those who had trespassed against the laws of foreign nations, or been convicted of a capital offence in any foreign kingdom; the last clause contains a proviso to that effect, and he had another clause ready to present, providing for the children of American citizens, born out of the United States.Rep Thomas Hartley, Pennsylvania, Continental Army Officer, Delegate to Provincial Congress, Delegate to Ratification Convention