I'm interested in measuring the frequency at which certain phrases
appear on the web, broken down by top-level domain. What I'd like to
do is enter a search term such as "fish and chips" and get results
that look like this:

.com 500,000 results
.org 25,000 results
.uk 50,000,000 results
.br 0 results

I'm not interested in the results themselves - just the frequency by
TLD. Is there a tool currently available that does this?

You could estimate your results by sampling.

For example, type your search in and see how many results the search
engine says matched your search string.  Then visit a certain number
of listed links and note which TLD the link belong to.  After sampling
a certain population of the sites, you can extrapolate how many of the
entire list come from each TLD.

This approach would not work well to test a large number of search
strings, but would work for a few search strings without too much
effort.  Of course if you need exact result rather than estimated
results, you'll need another approach as well.

You can try using Google's site: operator to restrict the results to specific TLDs.

  Google Search             Number Of Results
  ========================  =================
  fish and chips site:.com      1,320,000
  fish and chips site:.org        181,000
  fish and chips site:.uk         307,000
  fish and chips site:.br           3,950

It's not exactly what you want: You'd have to search every possible
TLD for a complete breakdown.