Growing a small olive tree in an outdoor plant box is entirely possible with the right conditions and care. Olive trees are hardy and adaptable, making them suitable for container gardening. Here’s what you need to know to ensure success:

1. Choose the Right Variety: Opt for dwarf or compact olive tree varieties like 'Arbequina' or 'Picholine,' which thrive in confined spaces.

2. Select a Suitable Plant Box: Ensure the box is large enough (at least 24 inches deep and wide) with proper drainage holes to prevent root rot.

3. Sunlight Requirements: Olive trees need full sun (6-8 hours daily) to produce healthy foliage and fruit. Place the plant box in a sunny spot.

4. Well-Draining Soil: Use a mix of potting soil and sand or perlite to mimic the tree’s native Mediterranean conditions.

5. Watering and Fertilizing: Water sparingly—olive trees prefer dry soil between watering. Fertilize lightly in spring with a balanced, slow-release fertilizer.

6. Winter Care: In colder climates, protect the tree by moving the plant box indoors or insulating it during freezing temperatures.

With proper attention, your small olive tree can flourish in an outdoor plant box, adding Mediterranean charm to your garden or patio.