  Recent deep Chandra LETG+HRC-S observations suggest the possibility that RX
J1856.5--3754 is a compact star whose radiation radius is 3.8--8.2 km. In this
paper, we systematically calculate the mass-radius relations of quark stars
within the bag model. Assuming that RX J1856.5--3754 is a pure quark star, we
derive an upper limit on its mass for various sets of the bag-model parameters.
