The pressure dependence of the superconducting transition temperatureTc(onset) ofTl1.8Ba2.0Ca2.6Cu3.0O10+&dgr;(Tl-2223) has been measured under quasi-hydrostatic pressure (QHP) up to 5.0 GPa. TheTcincreases with increasing pressure at a relatively high rate and reaches a maximum at 255.4 K and pressure of about 4.3 GPa. This is the highestTcyet observed for any high-Tcsuperconductor. The total change inTcfrom ambient condition(Tc=129 K)to the high pressure applied can be greater than 126 K. TheTcabove 200 K was replicated several times in our experiments. The site of the maximum ofTcand the value ofdTc/dP=1.7 K/GPa(atP=0) agree with previous results obtained by D. Tristan Jover &etal; (Physica C218, 24 (1993)) and J. G. Lin &etal; (Physica C175, 627 (1991)), respectively. ©1998 American Institute of Physics.