Should I talk to my ex?

My current boyfriend of a month has a real jealous streak and doesn't want me to talk to the ex boyfriend that I broke up with for him for, though I've known this person as a friend for 5 years. Now that I've been dating this new guy I find that I miss my ex's friendship and our conversations a lot. I know that if my boyfriend found out I called or was talking to my ex again he would be enraged. I am open with him and told him early in the relationship that I was still communicating with my ex and he was very against this and unhappy about it. In order to make him happy I haven't talked to him or called him eventhough he's been calling and texting me. My current boyfriend was so fed up that my ex was still trying to talk to me that he sent him a message to back off and told him some false stuff (i.e, that I can't stand my ex and I tell my boyfriend now all that time that I just want him out of my life) Do you think I have to pick one side or the other and sacrifice the other? Is there no middle ground? I really adore my boyfriend now and feel like he's worth it, but do you think his jealousy is a little outrageous? (this was the boyfriend right before him... I realize I probably shouldn't have jumped relationships so fast and now I'm paying for it)