Is it possible to get a PhD Degree in from USA or Europe after doing Masters from India I am a Chemical Engineering Masters student from India and I wish to pursue a PhD degree from some reputed US or European Universities. 

I have heard from my seniors and from internet searches that generally good universities do not admit students who directly apply for a PhD after a Masters degree from India and expect them to take a Masters degree from their university before going for PhD. 

It maybe that such instances would have occurred for some particular cases and cannot be generalized, but as I said that it is just what I have heard over from people and I wonder if it is true. 

I have been searching all over the internet regarding this but quite a few websites exist where this question has been answered convincingly. So I thought to post it here in stack exchange so that I can get some better answers. Any help would be appreciated.
You can certainly pursue a Ph.D. in the U.S. after getting a Masters degree in India.  You can even go straight in from a Bachelor's degree.  I know a number of people who have done it in other fields---I expect chemical engineering should be the same, I just don't know as many chemical engineers.

Note, however, that the first stage of many American Ph.D. programs is either explicitly or implicitly a Masters, and you probably will not be allowed to skip that stage of the program, though you might be able to pass out of some early requirements, depending on particulars of your background and the requirements of the university.