Is there a US 1000 dollar bill?

Yes, but it's no longer in use. It featured a portrait of Grover Cleveland and was last printed in 1945, although all of those carried the series date 1934.

$1000 bills were rarely used at the time and are effectively gone from circulation today. NO Federal Reserve Notes have ever been declared invalid or withdrawn, so if you had one you technically could still spend it. It would be foolish though because they're worth more to collectors - anywhere from $1100 to over $2000 as of 04/2010.

Bills larger than $100 are no longer available from banks. President Nixon signed an executive order in 1969 suspending distribution of high-denomination notes as a way of fighting organized crime by making it harder to move large amounts of currency.

Yes. The US issued so-called "High Denomination" bills from the time of the Civil War until 1945. They were issued in $500, $1000, $5000, and $10,000 denominations. They didn't circulate much because even $500 was a very large amount of money at that time.

Distribution of these bills was halted in 1969 by a presidential order, in an effort to combat money laundering by making it harder to convert large sums into cash. They were never officially withdrawn so if you had one today you could still spend it, but most stores wouldn't accept anything that large and in any case it would probably be worth more - maybe a lot more - to a collector.