In this work, the sol gel synthesis, structural characterization, and transport properties of a new solid solution of the general formula LaxBi1-xFe0.5Cr0.5O3 (0.4 <= x <= 1) are presented. The solubility limit x has been determined and variation of the lattice parameters measured through profile fitting. The cell parameters, space group, and atomic positions, as obtained by the Rietveld refinement of X-ray diffraction data, are reported. This analysis and electron diffraction studies as well do not reveal any evidence of Fe/Cr ordering. Regarding the transport properties, magnetic and electric characterizations are described. The electrical response with the temperature and frequency has been studied, and a "positive temperature coefficient" for the resistivity has been found for temperatures between 270 and 400 degrees C. The magnetic behavior is striking because, for all materials studied, zero-field-cooling curves appear above field-cooling ones, an anomalous feature that is interpreted as being due to complex ferromagnetic/antiferromagnetic interactions in the B perovskite sublattice.