Present Chef Butcher with the fruit from a Lime Tree and be rewarded with a knife. You can obtain the seeds to grow a Lime Tree from Ms. Weeder by trading her one Pink Murex. Lime Trees take about five days to reach a fruit bearing age.
You need to complete favors for Chef Butcher. After completing these favors he will give you a knife and a chisel. The chef will ask for a lime and sardine and after you give him these he will give you the knife and chisel.