If the Makita model 6095d cordless drill is made the same way model 6408, here is how it may work for you. Disassemble the housing, removed the chuck along with the spindle assembly. Insert a 7/32 (or other size depending) allen wrench into the chuck, place the allen wrench in a table vice. Get a scrap of a terry towel to protect the spindle shaft. Clamp a needle nose vice grip on the spindle assembly.
(WARNING NOTE, if the 6095 is not made that same way the 6408, then proceed with caution) Turn the vice grip counterclockwise (contrary to other drills). With an great amount of force the chuck should be freed.
Unlike other drills, the Makita model 6408 does not have a screw inside the chuck to secure it to the spindle shaft. This may be true for many or all Makita models.
J. Whyman, September 2009