More info on your set-up would be helpful.
How is the cable box connected to the TV (type of connector)?
How far away from the box is the TV in the kitchen?
Do you have a wireless network in the house/apartment?
If you're in an apartment, do your neighbors have a wireless network?
What frequency does your cordless phone use, if you have one?
What types of inputs do you have on both TV's?
Knowing these things would be very helpful. Since you said 'HD' I'll take that as an HDMI connection. If that's the case, your best solution, if the kitchen isn't over 50' away. Is one of these:
Ultra ULT40264 Performance 1080p 2 Port HDMI Splitter
The wireless transmitter mentioned in the post above is a possible solution, as long as it's the only transmitter in that frequency range within 200'. Otherwise, you'll have problems with getting a signal.
Just so you know, the cable box is your tuner. No matter how many TV's are connected to it, the channel on the box is what they all get.
If you want to get different channels, you'll need another box. Or if you live in an area close to a city you can try one of these:
and get all of your local channels in HD for free and be independent of the cable box.