An interesting question with many possible choices. Hopefully I can boil it down for you here. Basically it comes down to deciding what you like to do, since you will be more satisfied if you like what you do. Did you select your college school because it was more theoretical or practical? Do you prefer working alone or with a team? How competitive are you? What is your financial situation?
Even excluding industries, some basic starting options you may be familiar with are:
What does each path entail?
Obviously if you want to work in research or development, you may want to consider a higher level degree, even to a PhD level. Think of research as creating basic innovations and development as trying apply some research concepts to the real world. It is much harder to put the time in for a PhD if you are trying to work full time.
A marketing path may lend itself to a later MBA. Speaking of MBAs, it is helpful for a process, project, or sales paths too. And an MBA can be earned while you are working.
I'd suggest that development and process engineering require more engineering prowess, while project engineering is more people, budgeting, and schedule management. Sales and marketing are more customer relations. Marketing tends to be more analytical than sales. Each of these jobs require a different mix of extroversion, practical application, and competitiveness. So there are paths for everyone!
In my personal career I mixed it up, having worked in all of these areas. Personally I've found product development and project management to be the most fulfilling. If you are as lucky, you will be given the option to try different things to see what you prefer. If you are not sure about the right path for you, you can (and should) ask your boss about this from a career development perspective.
Since chemical engineers are good with math, there is no reason why you can't move into the financial side of the business, if that is one of your likes. Or how about IT, or HR, or supply chain (purchasing/logistics)?
What about later?
Are you interested in a step up to management? Today it is almost imperative that you have an MBA, or at least a master's to step on that ladder. Many people do not like the extra stress of managing other people, providing assignments, reviewing work, mentoring, and disciplining. If you are one of those, management is not for you! If you want to try it, ask your boss if you can help train some newer people, and you will get a taste.
The great news is that a chemical engineering degree is a fantastic starting point for almost any career. Of course, I'm biased!