EEOC Claim?

What is the name of your state (only U.S. law)? Connecticut

I work for a financial firm which is headed towards some unavoidable layoffs. It has already been hinted to me that I'm in the crosshairs to be let go. But it's also been suggested that someone who is currently out on maternity leave - whose job has already been entirely phased out - may be put into my position while I'm shown the door. The logic for this as I was told is "because she has a new baby." Me, I only have three teenagers to support!

I've been with the company years longer than this woman and I make substantially less. I've never been issued a bad review. I'm also the oldest worker in the department and the only male.

All this makes me feel targeted. If this does come about, do I have a valid claim with the EEOC?

You would have to show that you were being chosen BECAUSE you were male and BECAUSE you are over 40. Simply being male and over 40 does not create a valid claim.