You will need both Cygwin and MinGW.

Open a Cygwin Bash shell and do the following:

.../chicken/mingw % export PATH=/cygdrive/f/SomeDir/MinGW/bin:$PATH # Note 1
.../chicken/mingw % sh autogen.sh
.../chicken/mingw % sh configure.sh C:/CHICKEN # Note 2
.../chicken/mingw % make CHICKEN=C:/CHICKEN/bin/chicken.exe # Note 3
.../chicken/mingw % make test # Note 4
.../chicken/mingw % make install

Note 1: Not needed if you installed MinGW in its default location of
C:\MinGW.  Please change the first step to indicate where MinGW was
installed (the first step assumes you installed MinGW in
F:\SomeDir\MinGW).

Note 2: The "C:/CHICKEN" is the install location.

Note 3: The "CHICKEN=...chicken.exe" is where an old version of
CHICKEN is so that we can bootstrap the Chicken compilation.

Note 4: This is optional.
