First production of an American comedy:

The Contrast (1787)
On April 16, 1787, Thomas Wignell appeared in the first professional production of a native American comedy -- The Contrast, a story about the "frivolous practices of the old world" in contrast to the "sturdy, vigorous forthrightness of new America."
Source: Cambridge Guide to American Theatre, Don B Wilmeth,

  Continental Congress bans theatre:

October 1774
On October 20, 1774, with war with the mother country imminent, the American Continental Congress banned "gaming, cock-fighting, exhibitions of shews [sic], plays and other expensive diversions and entertainments."
Source: History of North American Theater, Felicia Londré,

  Massachusetts bans "public stage plays":

April 1750
On April 20, 1750, the Massachusetts General Court banned "public stage plays and other theatrical entertainments" because they "discourage industry and frugality" and "tend generally to increase immorality, impiety and a contempt of religion."
Source: The Colonial American Stage, by Odai Johnson,

  First professional actor arrives in America:

In 1703, Anthony Aston, a professional actor from England, arrived in America and performed in Charleston and New York.
Source: The Making of Theatre History, Paul Kuritz,