Proper chromosome congression (the process of aligning chromosomes on the spindle) contributes to accurate and faithful chromosome segregation. It is widely accepted that congression requires kinetochore fibres (K-fibres), microtubule bundles that extend from the kinetochores to spindle poles. Here, we demonstrate that chromosomes in human cells co-depleted of HSET (human kinesin-14) and hNuf2 (human Ndc80/Hec1-complex component) can congress to the metaphase plate in the absence of K-fibres. However, the chromosomes are not stably maintained at the metaphase plate under these conditions. Chromosome congression in HSET + hNuf2 co-depleted cells required the plus-end directed motor CENP-E (centromere protein E; kinesin-7 family member), which has been implicated in the gliding of mono-oriented kinetochores alongside adjacent K-fibres. Thus, proper end-on attachment of kinetochores to microtubules is not necessary for chromosome congression. Instead, our data support the idea that congression allows unattached chromosomes to move to the middle of the spindle where they have a higher probability of establishing connections with both spindle poles. These bi-oriented connections are also used to maintain stable chromosome alignment at the spindle equator.