If we extended the concept of a kitchen room, which to me implies a permanent, human-built structure with four walls and a roof, to include a dedicated cooking space separate from the rest of the living and working space, then we first see kitchen cooking space with our hominin ancestors.
There is some debate, but H. erectus possibly began using fire for cooking more than a million years ago. We start to see more controlled use of fire, and the establishment of permanent hearths by 300,000 years ago in Israel, but the distinction in cooking and living space is not yet apparent.
By 100,000 years ago the practice of consistent, controlled use of fire was well established, and the organization of living and cooking space begins to make slight changes. Neanderthals in Spain 50,000 years ago organized their caves in a specific manner. A brush windbreak blocked the entrance, there were separate places for bone and antler work, as well as defined sleeping spaces and dedicated hearths (Science 2009). The hearths were defined space to protect the fire, and made a cozy area for cooking that was defined for that specific area. Early Paleolithic sites like Le Lazert Cave and Bilzingsleben Cave show the placement of two hearths in the back of the cave, away from the doorway and separate from the bedding/sleeping area. For more free-standing structures, like huts constructed of mammoth bones in the Upper Paleolithic at Mezin in the Ukraine, the dedicated cooking space and hearths were confined to two corners of the hut (Klein 1999).
We may think kitchens are a new phenomenon, but our ancestors started separating their cooking space from their living and communal work space nearly 100,000 years ago.
Edit: Oops. I misread the Science article. The Neanderthal hearths at Abric Romani were well established, but we see them spread without the cave, and within different dedicated spaces for sleeping and tool manufacture. I edited my comment to reflect this change. The hearth placement in the back of the cave appears in the Lower Paleolithic and continues onward, though it is not ubiquitous until later in human history.
I am not an expert, but rather a somewhat well-read fan of homes and houses. (I'm a carpenter, so my interest is based in plenty of hands-on experience)
I agree that the idea of having the cooking take place in a different location is probably as old as cooking. Cooking is messy: hot, smokey, lots of smells and potential spills. You can see this at historical sites all over the world, where the kitchen area is in a completely separate building as soon as the inhabitants can afford to move it away.
Something interesting happens in 1600's Netherlands though. (I'm paraphrasing "Home: a short history of an idea" by Witold Rybczynski) There is the rise of what we would call the middle class, where the mid-level of the economy begins to form the direction of culture. Popular paintings of the time start to show domestic interiors, containing normal people doing normal things, instead of, say, mythological or religious epics complete with heavenly beings. The point here is that places like the kitchen started to become a place that wasn't hidden away but was shown as the center of the home. Rybczynski points to this as being the point at which a person's house became more than just a place to shelter and/or show off to others, but a personal refuge.
Home design still wrestles with the location of the kitchen, because cooking is still messy, but now (at least in current America) people don't want to isolate this process from the rest of their living. You see this with open kitchen plans and designs that merge dining rooms and kitchens.
(here's hoping that this response makes the grade...)
The BBC did a series on a number of rooms (bathroom, kitchen, etc.) that walks you through the history of the room, how it changed over time, and other stuff.
Really great stuff, and all available on youtube. Video 1 in the Kitchen series
There a great book by Bill Bryson called "Home" that goes into great detail about the history of the home and how each room came to be.
Can someone address actual usage of terminology equivalent to "kitchen"? I know the Latin term "culina" was used in Petronius' Satyricon in the 1st century AD. Is anyone aware of any earlier examples?