While I don't know for sure that this watch takes a 344 (the experts will have to ber trusted for that confirmation), I can tell you that according to "batterymart.com", the following batteries are its equivalent: SR1136SW, SR1136, V344, 242, SR42.
The important parameters are voltage, capacity, height and diameter. The 344 and its equivalents are 1.55V, 100mAh capacity, 3.6mm height and 11.6mm diameter. The 392 battery that Tim mentions is also 1.55V and 3.6mm height but it is smaller in diameter at 7.9mm and has a much lower capacity at 45mAh. Therefore, if the 344 is correct (and it sounds like it is), then the 392 will be smaller and possibly prone to moving around, and the lower capacity will probably result in a much shorter life.
Steve

: What battery does a Heuer 980.027 Dive watch take? It is the dual
: time with digital and analog circa 1983. I have an Energizer 344
: that is in it now, but I can't find one unless I buy one on
: eBay. I want to make sure that I am getting the correct one. The
: movement is the
: ESA Y2 900 231. Does anyone know the correct battery for this?

: Thanks

: Ken