1778 In The United States

• President of the Second Continental Congress: Henry Laurens (until December 10), John Jay (starting December 10)

January–March

• January 18 – The third Pacific expedition of Capt. James Cook, with ships HMS Resolution and HMS Discovery, first view O'ahu then Kaua'i in the Hawaiian Islands, which he names the Sandwich Islands.
• February 5 – South Carolina becomes the first state to ratify the Articles of Confederation.
• February 6 – American Revolutionary War: In Paris the Treaty of Alliance and the Treaty of Amity and Commerce are signed by the United States and France, signaling official recognition of the new republic.
• February 23 – American Revolutionary War: Friedrich Wilhelm von Steuben arrives at Valley Forge, Pennsylvania and begins to train the American troops.
• March 18 – American Revolutionary War – Battle of Quinton's Bridge

April–June

 

• May 1 – American Revolutionary War – Battle of Crooked Billet
• May 17 – American Revolutionary War – Battle of Thomas Creek
• May 20 – American Revolutionary War – Battle of Barren Hill
• May 30 – Benedict Arnold signs U.S. oath of allegiance at Valley Forge.
• June 24 – A total solar eclipse takes place across parts of the U.S. from Texas to Virginia.
• June 28 – American Revolutionary War – Battle of Monmouth: George Washington's Continental Army battles the British general Sir Henry Clinton's army to a draw near Monmouth, New Jersey.

July–September

 

• July 3 – American Revolutionary War: the Battle of Wyoming, also known as the Wyoming Massacre, takes place near Wilkes-Barre, Pennsylvania, ending in a terrible defeat of the local colonists.
• July 4 – American Revolutionary War: George Rogers Clark takes Kaskaskia.
• July 27 – American Revolution – First Battle of Ushant: British and French fleets fight to a standoff.
• August 29 – American Revolutionary War: The Battle of Rhode Island takes place when the Continental Army attempts to retake Aquidneck Island from the British.
• September – The Massachusetts Banishment Act, providing punishment for Loyalists, is passed.
• September 17 – The Treaty of Fort Pitt is signed, the first formal treaty between the United States and a Native American tribe (the Lenape or Delaware).
• September 19 – The Continental Congress passes the first budget of the United States.

October–December

 

• October 6 – American Revolutionary War – Battle of Chestnut Neck
• November 11 – American Revolutionary War: Cherry Valley massacre – British forces and their Iroquois allies attack a fort and the village of Cherry Valley, New York, killing 14 soldiers and 30 civilians.
• November 26 – In the Hawaiian Islands, Capt. James Cook becomes the first European to land on Maui.
• November 30 – American Revolutionary War: Continental Army in winter quarters at Middlebrook Cantonment, New Jersey.

Undated

• The first settlement is made in the area of what is now Louisville, Kentucky by 13 families under Colonel George Rogers Clark.
• Phillips Academy, a prestigious secondary boarding school in the United States, is founded by Samuel Phillips Jr.
• The term "thoroughbred" is first used in the United States in an advertisement in a Kentucky gazette to describe a New Jersey stallion called Pilgarlick.

Ongoing

• American Revolutionary War (1775–1783)
• Slavery in the United States

• January 6 – Thomas Lincoln, farmer and father of President Abraham Lincoln (died 1851)
• February 22 – Rembrandt Peale, artist and museum keeper (died 1860)
• April 11 – John Johnson, early leader in the Latter Day Saint movement in Ohio (died 1843)
• April 27 – Gideon Lee, politician (died 1841)
• May 3 – David Wilder, Jr., politician (died 1866)
• May 15 – Enoch Fenwick, Jesuit priest (died 1827)
• August 1
  • John Collins Warren, magazine founder (died 1856)
  • Mary Jefferson Eppes, Thomas Jefferson's younger child (died 1804)
• August 2
  • Jabez Delano Hammond, politician (died 1855)
  • Robert Richford Roberts, bishop (died 1843)
• August 3 – Jessup Nash Couch, politician (died 1821)
• August 4 – John Hunter, politician (died 1852)
• August 15 – John Tanner, early Mormon leader (died 1850)
• August 18 – Silas Condit, politician (died 1861)
• August 26 – John Adams, United States House of Representatives member (died 1854)
• August 27 – Mary Whitmer, Book of Mormon witness (died 1856)

• June 12 – Philip Livingston, merchant and statesman from New York City (born 1716)
• November 11 – 30 people in the Cherry Valley massacre
• June 15 - William Henry Ferrell (born 1740) "killed by Indians in New Garden Settlement, Washington, Virginia, United States" Source: Ancestry.com

• Timeline of the American Revolution (1760–1789)