Kenya yakawana chinzvimbo cheODI pachayo zvichitevera kuita kwakasimba muNdebe yeNyika ya1996, makwikwi avakakodzera kuwana nzvimbo yechipiri muICC Trophy ya1994. Chikwata ichi chakatanga kutamba mutambo weODI neIndia mumakwikwi e1996 World Cup, makwikwi ayo akapiwa nyika yeKenya chinzvimbo cheODI chenguva pfupi, chikatamba mimwe mitambo mina mumakwikwi aya. Kukunda kwokutanga kweKenya muODI kwakauya mumutambo wavo wechina weWorld Cup vachipesana neWest Indies. VaKenya vakakunda mutambo uyu nemaruniti 73 asi pakupedzisira vakapedza vari vekupedzisira muboka A. Kenya kubvira ipapo yakakwikwidza kumakwikwi mana eCricket World Cup. Vakasvika padanho remapoka mumakwikwi a1999, makwikwi a2007
uye makwikwi a2011. Pakwikwi reCricket World Cup ra2003, rakaitirwawo muKenya, chikwata cheKenya chakapedza chiri chechipiri muboka ravo uye nekudaro chakakwanisa kuenda kunhanho yeSuper Sixes. Kenya yakapedza iri yechitatu muchikamu cheSuper Sixes uye yakakwanisa kuenda kuma semi fainari kwavakarasikirwa neIndia nemaroni makumi mapfumbamwe nerimwe. Chikwata chemuKenya chakatamba mitambo yeODI zana nemakumi mashanu nemana neyekupedzisira ichisvika muna 154. Thomas Odoyo naSteve Tikolo vakatamba mitambo yakawanda yeODI yeKenya ne131 mumwe nemumwe. Tikolo ndiye akahwina mamakisi akawanda achitambira chikwata ichi 3369, ukuwo Odoyo ndiye akahwina mamakisi akawanda achitambira chikwata ichi 141.