My advice would be to get a Bachelor's in Mechanical engineering; then, a Master's in a field specific to Chemical Engineering if you're still interested at that point. That way, you can always float between both areas with good expertise under your belt.
I'm currently studying Mechanical Engineering and as the others have said, it's a very broad course and will allow you entry into many different fields. A lot of people don't know where they want to settle even years after graduating so being able to explore different options is great. A Master's will allow you gain those skills specific to your desired career path.
I might be a little biased since it is my major so take what I say from an objective stance. Goodluck with the decision and congrats on the offers.