A tough question. The field is very demanding, so be sure you really want to put several  years of your life into such a demanding field. The first thing to do do is find an advisor or mentor early in your undergraduate career and choose him carefully. Often people change advisors several times when the 'chemistry' doesn't work out (no pun intended -- It's a process of self-discovery that many chemists take.)

    If you do well as an undergraduate you can expect high rewards even with just a bachelor's degree.  Starting salaries can run as high as $40,000 per year. Still, according to the American Chemical Society 2001 Starting Salary Survey, almost half  off bachelor's graduates say they will continue with full-time graduate study or medical school.

     But first le'ts take a step backward and look at why students fail chemistry, for it very true but little known that this problem dogs even chemistry majors right into graduate school. Thinking hard about these failure issues can help you decide to avoid a career in chemistry -- or, better, will help you correct problems early on that might interfere with your sucess. It's hard, no question about it. and many prefer to steer clear of it. But you can increase your chances for success by avoiding some common errors  One problem is that the first few classes in a chemistry course are usually pretty easy and could lull you into a false sense of security. Do the work regularly, never miss labs or tutoritial sessions. If you slide over the basics, you'll quickly land in trouble. Set aside a small segment of time each day for chemistry. It will help you to gain long-term mastery. If you're forced to cram the night before,you havent been doing things right

Sometimes the cause of trouble is poor preparation in basic courses:

Insufficient Math Preparation
Don't go into chemistry until you understand the basics of algebra. Geometry and trig are especially important. Do problems daily and try to resist using a calculator. You will need to be able to perform unit conversions.

Another common problem is not reading ( or even buying!) the textbook

Contrary to what some fellow students might tell you there are NO courses where the text is useless. Get the textbook and read it faithfully! Ditto for any required lab manuals. Even if the lectures are fantastic, you'll need the book for the homework assignments. A study guide may be of limited use, but the basic text is a must-have.
Also don't psych yourself out. College students are always trying to cut the next guy down to increase their own chances. Don't listen to them. When I was in a college there was a bookworm who eventually made into medical school, partly by giving wrong advice to fellow students, pretending not to know how to do a problem when students would study in groups, etc.  If you convince yourself you'll fail then you will fail: a self-fulfilling prophecy.END you have prepared yourself for the class, you have to believe that you can be successful. Also, it's easier to study a topic you like than one you hate.

A caution: it is common to get together in groups to study problems; the danger here is that you'll tend to rely on others to shoulder the burden. And you'll learn very little.

     In general, there are many opportunites with a chemistry degree. Jobs abound in industry, or you can go right to graduate school. Don't look for faculty positions teaching chemistry however with only a bachelor's in chemistry. Even a master's degree offers little by way of teaching opportunities, though you might get  job at a small community college.

   The holy grail of course is a Ph.D. in chemistry. But bebore applying, think carefully about your own career interests and objectives. Getting a doctorate require at least four years and is in a way dangerous; the reason is that, as in so many other fields, many end up with that unglorious title "A.B.D." meaning all but dissertation. This way of putting it is a terrible euphemism however, as the dissertation is really what graduate school is all about and very few are impressed with "ABD's" anymore. You have to finish the dissertation. This applies both to finding faculty positions and to jobs in industry.  And in industry, a Ph.D. gives you far more independence in choosing your line of research.
    Chemists with only a bachelors degree tend to work under the close supervision of senior scientists, and this tends to be the case with MS level chemists as well. Note that most graduate programs in chemistry do not have a Masters degree option, and MS degrees are often only awarded to students who are required to leave a PhD program because of unsatisfactory performance..
  It should be encouraging to note that that doctoral programs in chemistry and in fact most field, normally fully support their students, usually through fellowships, teaching assistantships and research assistantships. All of these typically cover your tuition as well as living expenses.
     It is important to note that judging applications to graduate programs in chemistry is the job of the faculty in the department you are applying and not the admissions office. The standards that faculty use in making their admission decisions varies are fairly standard; they look for someone who they would want in their research group. So seek out this kind of experience as an undergraduate.  It hardly needs saying that you should cultivate a very good  relationship with your undergraduate teachers, as he will be providing your references to grad school. Sometimes your teachers will know personally the faculty who will be evaluting your application to grad schoo. This is more likely, the better your undergraduate school is. Of course, grades and GRE scores are equally important.

    Also, early start to read about graduate programs that are strong in the areas of chemistry that interest you. Check out their websites, look at various rankings of chemistry departments, etc. 

     Finally, here is a list of the top schools in chemistry:
  

UC-Berkeley

MIT

Caltech

Cornell

Texas

North Carolina

Chicago

UCLA

Yale

UC-San Diego

Texas A&M

Note: some schools, for one reason or another, have dropped off the list of top schools. Purdue for example, though never in the top ten, was at least among the better graduate schools until hit by observations of scandalous behavior by some  of their faculty members; it is best to avoid this school until these problems are resolved.