A broadband continuum generation is reported in a novel multicore microstructured optical fiber (MOF) where irregular air holes are randomly distributed in cladding. By launching ultrashort light pulses from a Ti:sapphire laser into a 190-mm-long fiber of this type, we have observed a group of continua generated from different cores, each with distinct color. 20-dB bandwidth of the broadest continuum is 1260 nm with an average power of 143 mW. The result confirms that the multicore MOF can be fabricated, with different dispersion profiles tailored for specific supercontinuum (SC) generation towards practical applications.