This isn't much help, but...

Ancestry has Naturalization Soundex index card:
(Soundex) T-255
Martin Tschanhenz, Naperville, IL
Vol.-A.-267
Circuit Court Naperville, IL
Born Germany
Naturalized 26 Mar 1864
Witness: Valentine Kreiger and Andrew S. Harroun
(This index covered Iowa)

Ancestry also had Passenger Index listing for Martin Tschanhenz in New York in 1854.

This looks like it might be his ship passenger record:
Martin Tschauheinz (that's the spelling), age 34 (c.1820)
arrived 8 Jul 1854 in New York aboard the "Stormaway" out of Havre.
http://castlegarden.org/quick_search_detail.php?p_id=8122725

A quick look at the Stormaway's lists for 1854 showed no other passengers with a name even phonetically like Tschauheinz.