Peak Ness has successfully named this plant Longan in a facebook comment. She does have a slight advantage though, what with living in Thailand and all.
According to Wikipedia, the names for this fruit in Chinese and Malay mean "dragon eye" and "cat eye" respectively. I would not argue with this assessment. Longan falls into the category of eyeball fruits.
Mark Kaplan guessed this fruit might be lychee or rambutan (also via facebook). You may remember rambutan from the very first Name This Plant. Lychee, also like the longan and rambutan, has an outer shell with an eyeball-like fruit inside. All three fruits are frequently sold on the roadside here in bunches still attached to small branch.
According to Purdue's horticulture web site, logan is often named in reference to the lychee:
"Closely allied to the glamorous lychee, in the family Sapindaceae, the longan, or lungan, also known as dragon's eye or eyeball, and as mamoncillo chino in Cuba, has been referred to as the 'little brother of the lychee', or li-chihnu, 'slave of the lychee'. Botanically, it is placed in a separate genus, and is currently designated Dimocarpus longan Lour. (syns. Euphoria longan Steud.; E. longana Lam.; Nephelium longana Cambess.). According to the esteemed scholar, Prof. G. Weidman Groff, the longan is less important to the Chinese as an edible fruit, more widely used than the lychee in Oriental medicine."Though I am a fan of the flavors of all these fruits, I am not a big fan of their consistency and eyeball-like qualities. I rarely eat them.