Please read the answer taking it for granted that the stone that you are talking about is in the gall bladder
. In other words, we are talking about a gall-bladder stone
1. If you do not have symptoms referable to the gallbladder
stone, you need not hurriedly go in for surgery. You can monitor the course of the stone by serial ultrasound scans (once every 6 months for initial 2 years, followed by once a year). Decision to operate can be taken anytime if the need arises during this period (e.g. due to continued dyspeptic symptoms like indigestion in the absence of acid reflux
(proven on endoscopy) / attacks of acute infection / jaundice
2. Medicines to dissolve stones are available in modern medical field, but practically not useful for various reasons. (a) The medicines have to be taken over a fairly long duration (6 months at least) (b) There is no guarantee that the stone will be dissolved. (c) Even if stone does dissolve, it may reform after the medicine is discontinued. The medicine can't be taken life-long (due to potential side effects).