Is this a CRT? Is the fault on the monitor itself or on a protective cover sheet?
If the answer is YES, DO NOT USE monitor. There is a very high vacuum in a CRT and a fault in the glass weakens the whole tube such that it could implode very loudly and with very unfortunate results. It is VITAL that you get this looked at/rectified without delay.
A surface chip is less likely to be as dangerous as a crack but even so, get it fixed.