In general, the graphics capabilities of mobile devices and web browsers are inferior to those available on a desktop machine. Thus, it sometimes takes some massaging of your Chief model to get a result that will work well in 3D Viewer.
Running out of memory in the 3D Viewer on a mobile device or the web can typically be attributed to one or both of the following:
1) High surface counts
2) Large image files used as textures.
Sometimes, leaving a few items out of an export can dramatically reduce the size of the export. If I'm having memory problems, I'll look for:
1) Symbols with lots of small, complicated surfaces. Things like 3D plants, chandeliers, intricate millwork, accessories with inlaid patterns, etc. often contain A LOT of surfaces and can be hidden or removed without sacrificing much visual appeal. Look for items with a lot of detailed, curved surfaces. You can put them on their own layer and turn the layer off for export.
2) High definition textures. I once came across a model that included an open magazine with a picture that took up half the page. The image for the picture had a resolution of 4096x4096, which is much bigger than the resolution of the iPad on which it was going to be displayed. A single image that size could take up more than 60 MB of memory in the renderer (even though the file itself might be smaller due to compression). For a small detail that is unlikely to ever take up a large portion of the screen, a much smaller image (say, 128x128) would suffice. In my case, I chose to delete the magazine before exporting.