I am US-born and my parents are from Taiwan. I successfully got a Taiwan passport two years ago. There was a good bit of confusion and bureaucracy involved but it was doable, so I wrote this guide. Hope it helps others who want to do the same.
[Unfortunately as a new user I’m not allowed to post more than 2 links so I’ve removed the links, mostly to Wikipedia. I’ll try to edit this post and add them later.]
ROC (Taiwan) Passports for Overseas Chinese
If your parents (or ancestors) are from Taiwan but you were born overseas, you may be automatically a Taiwanese national and therefore eligible for a Taiwan passport. This is not applying for citizenship; this is applying for a passport based on the nationality you already have!
Note that holding a Taiwan passport does not make you a Taiwanese “citizen”. Taiwanese nationality law defines “nationals” (國民, guómín), not “citizens” (公民, gōngmín). As an overseas-born Taiwanese, you are a “national without household registration” (NWOHR). Without household registration, your Taiwan passport is only as useful as a photo ID and travel document. Citizenship-type rights and responsibilities, such as right to vote, right to work, right to adobe, health insurance, conscription duties, etc. are restricted to those with a National Identification Card, which is in turn restricted to nationals with household registration.
Household registration can be obtained by living in Taiwan continuously for one year. That’s a different problem; see the guide “How to get Taiwan Citizenship - Primer, FAQ, and Resources” on this forum.
Applying for passport
You must apply for your passport from the Taipei Economic and Cultural Office (TECO) closest to where you reside. Each TECO office has a specific consular jurisdiction. Make sure you use the correct office!
Summary of instructions
In addition to providing the
- passport application form
- passport photos
- application fee
… you need to provide proof of an ancestor’s ROC nationality, together with proof of descent.
In the case where it’s one of your direct parents, this consists of:
4. your photo ID
5. your birth certificate (authenticated if necessary)
6. your parents’ marriage certificate (authenticated if necessary)
7. copy of one parent’s ROC passport (including photo) -OR- copy of parent’s household registration record (hùkǒu, 戶口).
If you were born before February 9, 1980, the ancestor must be from your father’s side (i.e. through the male line).
Authenticating documents
If a document originates outside your (local) TECO office’s jurisdiction, you will need to get it authenticated from that (remote) TECO office. For example, if you live in San Francisco, you were born in Indiana, and your parents were married in Pennsylvania, you must send your birth certificate to TECO Chicago for authentication, your parents’ marriage certificate to TECO New York for authentication—and then finally everything to TECO San Francisco. 
Note: “the legalized marriage certificate is valid only within 30 days after authentication, as for the birth certificate, within 60 days after authentication.”
Summary of instructions
You need to send
- authentication form
- The original birth certificate, death, the original certificate, marriage certificate original (county office issued)
- photocopy of your American passport, Taiwanese passport photocopy of your parents (with photo on that page),household registration record (hukou) is OK
- Fee-(Please buy one money order,payable to TECO)
- Sufficient postage or self-addressed and stamped envelope is required for returning the original document(s).