What is this brown sticky residue in my MacBook Pro charge port?
The battery is no where near that part - it's in the hand rest portion of the computer. Also, lithium polymer batteries don't really ooze liquids that would travel that far inside the computer, so it's probably the result of a spill near that area or just corrosion (rust) of the contact once the plastic covering has worn away.

However, any liquid or corrosion by the charging port should get checked out with someone moderately familiar with how electronics work - especially if you leave it plugged in and not on a fireproof table if you could be risking a fire in a house where people sleep or someone might not be aware enough to leave if trouble starts.

The time it would take for a technician to give your Mac the "all clear" would be 5 minutes and the screwdriver needed to pop the top. This is the equivalent of opening the hood and measuring the oil level in a car or truck.

I would clean off the area with a cotton swab and watch. If any more coloration or liquid arrives, take it in for service. Also, if the liquid were inside, you will see some coming out of the thunderbolt port as well. If a bright light and light magnification (or iPhone picture with flash) doesn't show any additional moisture, you might be safe with just some surface rust / a one time wet magsafe connector.