Narayan and Heyl ( 2002 ) have developed a theoretical framework to convert suitable upper limits on type I X-ray bursts from accreting black hole candidates ( BHCs ) into evidence for an event horizon . However , no appropriate observational limit exists in the literature . In this paper we survey 2101.2 ks of data from the Unconventional Stellar Aspect ( USA ) X-ray timing experiment and 5142 ks of data from the Rossi X-ray Timing Explorer ( RXTE ) experiment to obtain a formal constraint of this type . 1122 ks of neutron star data yield a population averaged mean burst rate of 1.69 \times 10 ^ { -5 } bursts s ^ { -1 } while 6081 ks of BHC data yield a 95 % confidence level upper limit of 4.9 \times 10 ^ { -7 } bursts s ^ { -1 } . This is the first published limit of this type for Black Hole Candidates . Applying the theoretical framework of Narayan and Heyl ( 2002 ) we calculate regions of unstable luminosity where the neutron stars are expected to burst and the BHCs would be expected to burst if they had a surface . In this unstable luminosity region 464 ks of neutron star data yield an averaged mean burst rate of 4.1 \times 10 ^ { -5 } bursts s ^ { -1 } and 1512 ks of BHC data yield a 95 % confidence level upper limit of 2.0 \times 10 ^ { -6 } bursts s ^ { -1 } , and a limit of > 10 \sigma that BHCs do not burst with a rate similar to the rate of neutron stars in these unstable regions . This gives further evidence that BHCs do not have surfaces unless there is some new physics occurring on their surface .