Keep Your Chin Up

This seems to be a reference to smiling thus equating a sagging chin to a frown.

According to Gary Martin at www.phrases.org.uk:

The first use of it that I can find is from the Pennsylvania newspaper The Evening Democrat, October 1900, under the heading Epigrams Upon the Health-giving Qualities of Mirth:

"Keep your chin up. Don't take your troubles to bed with you - hang them on a chair with your trousers or drop them in a glass of water with your teeth." - [they were easily amused in Pennsylvania in 1900].