Is it true that Mikhail Gorbachev was promised by NATO that they wouldn't expand beyond Germany in 1990?

Question

I heard a Russian analyst on PBS yesterday mention it. The expansion of NATO and the placement of missiles in eastern European nations by NATO in subsequent years would not have gone down well with Russia.

Answer 1

The US says no, Russia says yes.

Answer 2

America has a long history of reneging on its promises even amongst its friends.