EEOC Complaint or not?

I am a married male who works in an office with all males and only one (married) female. The two of us are friends (NOT involved in any way) and we are forced to work in a very close environment on a daily basis. There is one male co-worker who is very jealous because he has a "crush" on her and does not get the attention he likes from her (he is 51, believe it or not). As a result he has been spreading rumours that she and I are having an affair. In fact, he has made numerous lewd and obnoxious comments in mixed company and in my presence about her, to include suggesting that I am sleeping with her. The result is a very uncomfortable work environment to the point that I dread going to work. Does this constitute grounds to file an EEOC complaint?