Python with sympy, 69 bytes

...taking over from Gryphon's deleted submission.

from sympy import*
lambda n:sum(factorint(n+2).values())<3*isprime(n)

An unnamed function returning True for Chen primes and False otherwise.

Counts the factors of n+2 by summing its prime factor's multiplicities.

Note that 3 is multiplied by isprime(n) before the < comparison is made, so for non-prime n the code tests if n+2 has less than 0 factors (always yielding False), while for prime n it checks whether n+2 is prime or semi-prime.

Python with sympy,  69  56 bytes

-13 bytes thanks to alephalpha (by upgrading to sympy 1.1 and using primeomega(n+2) to replace sum(factorint(n+2).values()))

...taking over from Gryphon's deleted submission.

from sympy import*
lambda n:primeomega(n+2)<3*isprime(n)

An unnamed function returning True for Chen primes and False otherwise.

Counts the factors of n+2 by summing its prime factor's multiplicities.

Note that 3 is multiplied by isprime(n) before the < comparison is made, so for non-prime n the code tests if n+2 has less than 0 factors (always yielding False), while for prime n it checks whether n+2 is prime or semi-prime.