The work, which shows two rats holding protest signs, appeared in West Pallant behind another piece of graffiti by artist JPS, which appeared in 2018.
It appears the piece has been painted using spray paint and stencils, similar to the work of world-renowned graffiti artist Banksy.
The signs read, 'It's Priti awful' and 'Kill the Bill', a reference to recent anger at a proposed government bill that would restrict the right to protest.
Walter Francisco, cinema director and programmer at the Chichester Cinema at New Park, said: "I spotted it about two days ago when I was walking down South Street. I love the cat and it has been there for years - it's so cool.
"I thought to myself, 'I don't remember them being there'.
"To me, it's a Banksy and while I would like to believe that it is Banksy but realistically it is almost certainly not - just someone doing some clever street art and it goes very well with the cat.
"I love the street art in Chichester and wish there was more of it. It's great."
A version of this story was originally published by our sister title, the Chichester Observer