In doing some research into early eclipse observations from aircraft with Bob Morris I uncovered an article from 1914 in the NY Times. At the time there was an eclipse chaser named David Todd who was an astronomer at Amherst College. It seems he either had a fan at the Times or maintained regular correspondence with them regarding astronomical items of interest and his eclipse pursuits.
In 1914 David Todd proposed to follow the eclipse in Russia using an airplane capable of 120 miles per hour. He hoped to induce more speed from the plane by descending rapidly. His goal was to increase his observation time by several minutes. Towards this end he arranged for the equipment and started his journey.
The article caught my eye because it says his proposal was akin to "chasing the sun" - the earliest use of the word chasing with relation to solar eclipses that I've found in published media.