Wear's the problem?
Er, no. The top gear on your bike should be able to take ‘heavy load’ without complaint. Top road sprinters such as Mark Cavendish use their highest gears, apply a very heavy load to the transmission, and would not be best pleased to find it skipping midway through the final gallop. Furthermore, the smallest sprocket generally gets little use and should wear slowly. Finally, it is unlikely you have worn out a chain in 300 miles. The most likely culprit for the symptoms you describe is poor rear derailleur adjustment. Look at the outside throw screw first – it’s typically marked with an H.
Cycle’s Technical Editor