Why not to use having found a counter offer at another job as a bargaining chip with your current employer:
Watch the brief video here: How To Deal With Counter Offers (video)
Have you ever leveraged an offer from another company to get a raise at your current job? (I have not but got a job where someone use the position to stay with her current employer at a higher pay rate.)
If so, how did it go with your current employer, or did you end up taking the new job?