This means the frame is too narrow to hold the line, which can happen for a variety of reasons. IF text shows on the first line as you start to type, then disappears after a number of characters, you've got a setting that is preventing the text from breaking at the end of a line, possibly No Break applied to all text, or you have hyphenation turned off and are using non-breaking spaces (I see that a lot in imported Word files). If you never see any text, then it's probably an indent problem, either a frame attribute, or more likely the paragraph indent settings for the style or applied to the text as local formatting (saw that one the other day, also in an imported Word file).
I checked for non-breaking white space, and that doesn't seem to be the problem. Further, if I copy a text frame to a new document everything appears correctly. Copying a text frame from a new document that works correctly to the existing (CS 4) file causes it to complain about being overset suddenly. So, does this suggest it's a paragraph breaking or indentation problem? Where do I find these settings? I haven't had much luck so far.
There's so many variables. If you like you can host the file on yousendit and provide a link or PM with a link and I'll take a look at it.
It could be anything from oversized text, to Adjust Scaling Percentages, to keep options, to no break, to settings in the paragraph style, text wraps etc. etc. etc.