I have heard that Genesis chapter one and Genesis chapter two are
contradictory stories of the creation, written by two different authors.
Is this true?

No and maybe.

No to the first question. Genesis chapter one is the story of the creation
of the universe and more specifically of the earth and the life on the
earth. Genesis chapter two is the story of the creation of Adam and Eve.
The second chapter of Genesis covers one small part of one of the six
“days” of creation. There is no irresolvable contradiction between the two
creation accounts. Many have claimed that there is, but the supposed
contradictions disappear if one simply starts the account of the creation
of Adam and Eve with Genesis 2:7 (remember that the chapters in our Bibles
are arbitrary divisions, not included in the original writings).

As for the second question, that would require speculation. No one knows
who wrote Genesis. Although tradition holds that Moses wrote Genesis, the
evidence is that at most he may have been involved in putting it in its
final form, but almost certainly he was not the actual original writer of
the entire book. The historical content of Genesis bears signs of
authorship well before the time of Moses.

Many Bible scholars claim that the writing style of the first and second
chapters of Genesis are quite different, supporting the claim that there
were two separate authors. In answer to this, it can be said that this is
not an unreasonable explanation of the facts, but it remains unproven.
Either way, whether by two authors or one, there is no contradiction
between Genesis chapter one and chapter two.

Further discussion of this question is found in the article What About
Genesis?

John Oakes