Emergency services were called to the scene on The Fleet at around 9.30am.
Paramedics issued first aid and oxygen to the elderly patient before she was taken to hospital.
The accidental fire, caused by a chip pan, completely destroyed the kitchen.
The remainder of the house suffered minor smoke damage.
West Sussex Fire and Rescue Service have since issued a warning about kitchen fires.
A spokesperson said: “If you do have a fire in the kitchen, don’t take any risks - get everyone out of your home and call 999.
“If a pan catches fire: don’t move it - it is likely to be extremely hot; turn off the heat if it’s safe to do so, but never lean over a pan to reach the controls; place a fire blanket over the pan, if you have one; don’t use a fire extinguisher on a pan of oil - the force of the extinguisher can spread the fire and; leave the pan to cool completely if you have put the fire out.”
More information can be found online at West Sussex Fire and Rescue