We report the existence of a very large new family of two-component composite optical Thirring solitons which is solely supported by cross focusing of two optical beams, that is due to giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor. We identify a wide parameter space of power and spatial widths, which permits the existence of such stationary solitons. Direct numerical simulations of the coupled nonlinear equations that describe such solitons have substantiated analytical results. (c) 2006 Elsevier B.V. All rights reserved.