The invention provides seed and plants of the pea line designated 08560865. The invention thus relates to the plants, seeds and tissue cultures of pea line 08560865, and to methods for producing a pea plant produced by crossing a plant of pea line 08560865 with itself or with another pea plant, such as a plant of another line. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of a plant of pea line 08560865, including the seed, pod, and gametes of such plants.