Oh it can so be done.
I started running at 310# and would do a mile to a mile and a half 3 times a week then I joined a running group and 6 months later I ran my first half marathon.
Now (a year after that half) I am 245# and have done many 5k's 10k's, a 25k and this weekend is another half marry.

I say to look into the C25K plan HERE It will work you up to a 5K without killing you then after that just build your base miles up.
But first go to a running store (not a mall shoe store) and get fitted for the right shoes. That is the key to not getting hurt. Then when you start running, do not worry about your speed. If you try to go to fast right away you will hurt yourself. Take it slow and easy. The speed will come. My first 5K took me 36 minutes my last one I did in 25. The 15.5 mile race (25K) I did it with a 9:22 a mile average pace.. Not to bad for a guy my size. But then agian, I run 20 - 40 miles a week.