If you want an exact equivalent to
chomp, the first method that comes to my mind is the awk solution that LatinSuD already posted. I'll add some other methods that don't implement
chomp but implement some common tasks that
chomp is often used for.
When you stuff some text into a variable, all newlines at the end are stripped. So all these commands produce the same single-line output:
echo "$(printf 'one\ntwo') done"
echo "$(printf 'one\ntwo\n') done"
echo "$(printf 'one\ntwo\n\n') done"
echo "$(printf 'one\ntwo\n\n\n\n\n\n\n\n\n\n') done"
If you want to append some text to the last line of a file or of a command's output,
sed can be convenient. With GNU sed and most other modern implementations, this works even if the input doesn't end in a newline¹; however, this won't add a newline if there wasn't one already.
sed '$ s/$/ done/'
¹ However this doesn't work with all sed implementations: sed is a text processing tool, and a file that isn't empty and doesn't end with a newline character is not a text file.