I have had 3 miscarriages in 1 yr. I found out that I'm pregnant. What are the chances of this being a viable pregnancy?

Good. Hopefully some evaluations have been performed to determine if: your uterus is normally shaped, thyroid is normal, Progesterone levels are normal, your blood clotting studies are normal, and that both you and your partner have normal chromosomes.
Depends on cause. I usually recommend that once you've had two miscarriages that you ask your ob/gyn to do a work up to look for causes of repeat losses. These include looking for lupus like syndromes, genetic issues, low Progesterone and blocked fallopian tubes. You should also eliminate any bad habits before you conceive and take prenatal vitamins up to 3 months before conception.
See doctor. Patient with multiple miscarriages may have a lupus anticoagulant, or uterine abnormality, so check with you ob/gyn doctor , there is a possibility to have another miscarriage.