Get a structural engineer to review the home plans and inspect the home. Determine if the galley kitchen wall is load-bearing. If it is, he will develop a plan to replace the support beam points so the room is opened but you don't create a structural weak point.
Apply for a city building permit for the changes. File the plan for changes developed by the engineer and file any fees associated with the permit.
Remove the cabinets and tear down the dry wall exposing the bones of the wall and all electrical, plumbing and gas outlets, as well as noting which points are the weight-bearing points.
Replace the wall top with a support beam. The beam can be wood or steel. Ask the engineer what he recommends for the size of the wall and the structural needs. The beam fits along the top, wedged and attached to the room end posts.
Install a column in at the locations where weight loads were supported. You may need more than one column based on the engineer's calculations. The column sits under the support beam.
Remove the original wall framing once the columns and support beams are secured in place and reviewed by the engineer.
Have a licensed plumber and electrician move and re-wire plumbing, gas or electric points.
Install a kitchen island or table for added counter and workspace in the kitchen but still giving you open access to the next room.