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We show that r-mode instabilities severely constraint the composition of acompact star rotating at a submillisecond period. In particular, the onlyviable astrophysical scenario for such an object, present inside the Low MassX-ray Binary associated with the x-ray transient XTE J1739-285, is that it hasa strangeness content. Since previous analysis indicate that hyperonic stars orstars containing a kaon condensate are not good candidates, the only remainingpossibility is that such an object is either a strange quark star or a hybridquark-hadron star. We also discuss under which conditions sub-millisecondpulsars are rare.

A compact star rotating at 1122 Hz and the r-mode instability