The introduction of the Competency Based Curriculum (CBC) in Kenya by the government was seen as a positive innovation and a paradigm shift from the examination-oriented curriculum of 8-4-4 to the assessment of learners’ competencies through Competency Based Assessment (CBA). The objective of this study was to identify the challenges facing the Competency Based Assessment (CBA) in the Competency Based Curriculum (CBC). The study adopted a descriptive research design from a target population of 385 grade six teachers of which a sample of 120 teachers were selected through simple random sampling within Nairobi County, Kenya. A structured questionnaire was administered to the teachers to collect information about the challenges hindering the effective implementation of Competency Based Assessment (CBA) in the current Competency Based Curriculum (CBC). Validity and reliability of the study instruments were established through consultation with experts, triangulation and piloting. The structured questionnaire was piloted in one of the schools outside the sampling frame and reliability of the Cronbach's alpha was found to be 0.86 making it suitable for collection of information. The data was analyzed using descriptive statistics and the study findings presented in form of frequency tables, means and graphs. The study findings show that there is slow pace of transition of learners in the 22.214.171.124 Competency Based Curriculum with a transition uncertainty after grade six. It was further noted that the challenges facing the CBA implementation include lack of clear educational policies for effective implementation of the CBC curriculum, lack of validity and reliability of learners` scores, lack of ICT infrastructure, lack of adequately trained teachers, and negative attitude among educational stakeholders towards the new curriculum. The Ministry of Education should provide adequate resources for the effective implementation of CBC and CBA. The government of Kenya should enact educational policies to aid in the effective implementation of the new curriculum.