OPening a pdf in Chrome is performed on desk top by means of the Chrome PDF Viewer plugin. Chrome on Android does not support plugins. However, there's nothing to stop you installing Firefox and using that instead. Assuming that you have a PDF view of some kind installed on you device, the first time that you access a PDF in Firefox it will off er you the option of choosing the viewer or downloading it. You can either choose to use the viewer once only or always. Obviously, whichever methods you use, the file is downloaded anyway (just as it is in Chrome for Windows), the only differences being that (A) it will open automatically, and (B) it will be downloaded to a temp folder and removed late, unless you save it from within the viewer.
You can get Firefox here:
https://play.google.com/store/apps/details?id=org.mozilla.firefox