Chem GRE and school list?

[Disselkyle]

Hey everybody! I'm a rising senior applying for grad school in inorganic chemistry for Fall 2017. Brief resume:

Chemistry (ACS certified) and Chemical Engineering double major at small liberal arts college

GPA 3.86; chemGPA 3.75; GRE 166V/170Q; chemGRE 720 (56%)

2 summer's research experience, one at small liberal arts college, other at large state university (mid-20s ranked)

First author on a paper submitted to JPCA

Two questions: First, is my chemGRE low enough that I should retake it if I want to get into the best schools? Second, how does this school list look?

Top Tier: Caltech, UC Berkeley, UIUC
Mid Tier: Cornell, Princeton, Columbia, Rice, WUSTL
Fourth Tier:NYU, Notre Dame
 

[phenol]

Your qualifications look pretty good -- solid GRE and GPA and a first-author paper put you in a good position for basically all the schools you've listed.  Your Chem GRE is a concerningly low, but I'm not sure it'll be enough to single-handedly disqualify you from getting in.  It's the only obvious weak spot I can see in your application (assuming you have solid LoRs).

[Mediocrity]

I love that Princeton is mid-teir, lol. Your stats look great and I don't think your ChemGRE will hurt. First author paper will help that a lot, but then again, I don't go to CalTech, so maybe the score could hurt?