Random shutdown on a 15" macbook pro

Question

Hello, my macbook pro has started to randomly shutdown. The battery does not seem to charge much beyond 0% either. Here is the battery information from System Profiler -- is it likely just a battery issue?
Model Information:
Serial Number: Sony-ASMB012-356a-75f4
Manufacturer: Sony
Device name: ASMB012
Pack Lot Code: 0003
PCB Lot Code: 0000
Firmware Version: 102a
Hardware Revision: 0400
Cell Revision: 0303
Charge Information:
Charge remaining (mAh): 0
Fully charged: No
Charging: Yes
Full charge capacity (mAh): 1674
Health Information:
Cycle count: 309
Condition: Good
Battery Installed: Yes
Amperage (mA): 1945
Voltage (mV): 11875

Answer 1

It's picking a particularly bad way of telling you - your MBP should never just shut down - bug given your charge capacity seems significantly down from what you should be able to achieve I'd say yes, it looks to be a battery issue.
How old is your Mac?
Your battery should retain about 80% of its charge capacity after 300 cycles, and since you only have 309 cycles, your battery seems to be much below that.
If you've an Apple Store nearby and you're under warranty or AppleCare you may want to ask about it - they might replace your battery at no charge, depending upon a wide variety of factors.