The town was named after Olivet, Michigan, the native home of first settlers.

[7] The first county courts were housed in a Methodist church; a permanent courthouse was built in 1881.

[8] According to the United States Census Bureau, the town has a total area of 0.15 square miles (0.39 km2), all land.

[9] Olivet lies north of Lonetree Creek and is on the west bank of the James River.

The racial makeup of the town was 90.00% White, 2.86% Native American, and 7.14% from two or more races.

There were no families and 3.4% of the population living below the poverty line, including no under eighteens and 6.5% of those over 64.

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