The United States Supreme Court convenes for the first time in the Merchants Exchange Building in New York City. This was, at the time, the capital of the United States. John Jay is Chief Justice and there will be a total of just six Supreme Court justices.
Technically the United States Supreme Court had been called to assemble the day before, but Chief Justice John Jay experienced problems with transportation so it is only today that the court can actually meet. This first sessions is primarily about sorting out the duties and powers of the United States Supreme Court; the first actual legal case won't be heard until 1792.