Some of the details I say may very well be wrong but I have a loose
understanding of the law I'm talking about and would like more
information.  What I've heard is that when Texas became a state, the
federal government wanted the land to be split up and allow for new
states to be created, so a federal law was passed which basically said
that if 100,000 (again with details, this number may be different)
people got together in Texas and demanded their own state, a piece of
Texas would be cut up and that would be a new state in the union. 
This apparently was part of the compromise in Texas becoming a state
and this law apparently is still active on the books, however, no one
has actually utilized it.

Basically I want to know if what I was told was a true story, and if
so, more information on this law and the history surrounding it. 
Thanks!

Dear questioneverything1-ga, 

The version of the story you?ve been told is a bit garbled, but the
underlying fact is true. Yes, Texas does theoretically retain the
right to divide itself into four states in addition to the state of
Texas, for a total of five states. This comes from the ?Joint
Resolution for the Annexing of Texas to the United States," a
resolution passed by both houses of the U.S. Congress in 1845 prior to
admitting Texas to the union. The resolution remains in effect.
However, that?s not to say Texas is going to be breaking up any time
soon. Even though the right to do so exists, there are significant
obstacles to it ever happening in reality.

Here are some links to further reading on the subject, as you asked: 

The full text of the Joint Resolution for Annexing Texas to the United
States, 28th Congress, Session II 1845, Volume 5, Resolution 8, pp.
797, 798 is available in electronic format at the Library of Congress.
Click on the link below, and when you get to the page, 
look on the lefthand side, 
click on ?List of Public Acts,? then 
under the radio button labeled ?Turn to Image,? type in ?797,? 
hit ?Enter? and 
scroll down the page to the bottom, where the text of the Resolution begins. 
The part about dividing the state is on p. 798, however, right after
the word ?Third.?
http://memory.loc.gov/ammem/amlaw/lwsllink.html

?DIVISON OF TEXAS,? an article from the Handbook of Texas Online,
gives some historical background on the law.
http://www.tsha.utexas.edu/handbook/online/articles/DD/mqd1.html

?LET?S MESS WITH TEXAS, ? an essay byVasan Kesavan and Michael Stokes
Paulsen, published in the Texas Law Review, gives a more modern and
slightly irreverent look at the matter:
http://www.utexas.edu/law/journals/tlr/abstracts/82/82kesavan.pdf

     *Note: the above article is in pdf format which requires Adobe
Acrobat Reader to view. If you don?t already have it, you can download
a free copy here:
www.adobe.com/products/acrobat/readstep2.html
   
?FIVE LONE STARS,? is a blog entry referencing the above article, also
on topic and also a bit tongue-in-cheek.
http://beldar.blogs.com/beldarblog/2004/08/five_lone_stars.html
 
And finally, Snopes.com has a fairly good overview of the matter: 
http://www.snopes.com/history/american/texas.asp
   
I hope this fully answers your question and gives you the information
you?re looking for. If not, or anything remains unclear, please use
the ?Request Clarification? feature to ask before rating and closing
your question.

Sincerely,
Byrd-ga

Search terms used: 

[texas statehood annexation law partition OR divide ?divorce]
["Joint Resolution for the Annexation of Texas"]

This was a satisfactory answer, thanks for the research!

Texans  - like Bavarians in Germany -  are now much too proud of being
part of the largest of the lower 48 states.
But it is a great idea.

The Texans really should think about, following the lead of the Soviet
Union after the war.  The Ukraine, White Russia and, I believe a
couple of other members of the USSR were recognized as individual
members of the UN, but not very independent ones.  (I have heard
firsthand that it at least one representative of such a UN member who
ventured to express an opinion was ushered from the table and never
returned.)

SO, if Texas got its act together, it could become five states:  ten
US senators, probably a couple of more Congressmen, AND much more
leverage in presidential elections.

Horrid thought, especially at present.
Oh, I see the "Let's mess with Texas" essay came to the same conclusion.

Kind of takes the fun out of posting comments when the Researcher has
done such a thorough job.  Just another lesson about reading
everything first.