Aside from the chest, how is the fit for the rest of the coat? Shoulders/upper back, torso length, sleeve length, diameter of the coat at the waist and hip? Those could drive your decision.
When it comes to matching fabric colors, black is probably the hardest. If it is only the chest that needs to be larger, AND you can match the fabric, you could split the side seams and insert three inch wide (plus seam allowances) pieces of fabric. These would have to be tapered into the underarm seam as well. You would now have two "side" seams that would be somewhat hidden when your arms are at your sides. Tailored suit jackets are made this way. If you aren't trying to recreate this exactly, it might be easier to find a contrasting or complementary color.
If it is more than just the chest measurement that needs adjustment, it would be easier to recreate the coat in the correct size.
Unfortunately, it is very difficult to make things larger - it is much easier to make things smaller.