The ASVAB score is just one parameter.
The real indicators are the combination of specific line scores from the ASVAB.
The sheet with your test results is the 680-ADP. Below the line scores are calculations, and the two for nuclear power are NUC and EL. These are the sum of VE + AR + MK + MC or AR + MK + EI + GS, and either needs to be >= 252 to NOT have to take the NAPT exam. Either calculation, plus the NAPT score, must be >= 290 to be eligible for nuclear power.
VE is verbal, AR is arithmetic reasoning, MK is math knowledge, MC is mechanical comprehension, EI is electronic information, and GS is general science.
Even an ASVAB of 75 can have line scores that are high enough for nuke, if the scores are high enough in the right areas.
With a BS in chemistry, you want to go ahead and speak to the officer recruiters in your area. Your regular enlisted recruiter will try, overtly or otherwise, to steer you away from them, but with a BS you're supposed to get an interview with an officer recruiter automatically. If this doesn't happen, let me know, and I'll fix it. I am the nuclear field recruiter for the Pacific Northwest, and can answer any question you may have. Keep in mind, the typical Navy recruiter is not a Nuke, and is therefore hesitant to speak about Nuclear subjects, which is why all parts of the country have NF recruiters at each recruiting district headquarters. I can also put you in direct contact with your local NF recruiter.
Get all your questions answered before you sign anything!