A method for fabricating a ceramic structure provided with a ceramic composite coating thereon formed by chemical vapor deposition, comprising the steps of contacting a ceramic substrate capable of withstanding a temperature of at least about 1,200.degree. C.-1,500.degree. C. with the gaseous mixture of methyltrichlorosilane, titanium tetrachloride and the carrier gas of hydrogen, and heating the substrate and gaseous mixture to a temperature sufficiently to thermally decompose the methyltrichlorosilane and the titanium tetrachloride to effect the codeposition of a matrix phase of silicon carbide and a dispersed intermetallic phase of titanium disilicide.